# Geometry Chapter 12. Volume. Surface Area. Similar shapes ratio area & volume

Save this PDF as:

Size: px
Start display at page:

Download "Geometry Chapter 12. Volume. Surface Area. Similar shapes ratio area & volume"

## Transcription

1 Geometry Chapter 12 Volume Surface Area Similar shapes ratio area & volume

2 Date Due Section Topics Assignment Written Exercises 12.1 Prisms Altitude Lateral Faces/Edges Right vs. Oblique Cylinders 12.3 Chpt 12 Packet Pg(s) # 12.2 Pyramid Vertex Slant Height Chpt 12 Packet Pg(s) 12.3 # Cones Spheres Chpt 12 Packet Areas and Volumes of Similar Solids Pg(s) # Written Exercises beginning on Pgs 478, 485, 492, 500, 511 Pg 496 (Self Test 1) # 1-3, 5-8 Chapter 12 Extra Practice Pg 513 (Self Test 2) #1-6 Pgs (Chpt Rev) #1, 3-5, 7-19 Pgs 519 (Chpt Test) #1-16 1

3 Chapter 12 Formulas Note: The formulas with stars (**) next to them ARE given to you on all assessments! Prism LA = ph OR SA = LA +2B Pyramid LA sum area of lateral faces LA = 1 2 pl OR LA sum area of lateral faces SA = LA + B V = Bh ** V = 1 3 Bh Cylinder Cone ** LA = 2 rh ** LA = rl SA = LA +2B SA = LA + B ** V = Bh ** V = 1 3 Bh Sphere Hemisphere ** A = 2 4 r LA = 2 2 r ** V = 4 3 r 3 r 3 SA = 2 V = 2 3 r 3 2

4 Prism: Section 12-1 Define the following terms. Draw a prism and label each term in the diagram. Prism: Diagram Base(s): Altitude: Lateral Faces: Lateral Edges: 3

5 What is the difference between a right prism and an oblique prism? Draw a diagram. What is the difference between lateral area and total area? What is a cube? Draw a picture. 4

6 Pyramid: Section 12-2 Define the following terms. Draw a pyramid and label each term in the diagram. Pyramid: Diagram Vertex: Slant Height: Label the following the diagram: Base, Altitude, Lateral Faces, and Lateral Edges A E D F B 5 C

7 What is a regular pyramid? What is the difference between an altitude (height) and a slant height? Cones and Cylinders: Section 12-3 Diagram of Cylinder: Diagram of Cone: Label the height and radius in both diagrams. Label the slant height of the cone. How are the prism and cylinder similar? What is the difference? How are the pyramid and cone similar? What is the difference? 6

8 Spheres: Section 12-4 What is a sphere? Draw a diagram? Ratio of Areas and Volumes of Similar Solids: Section 12-5 If the scale factor of two similar solids is a:b, then the ratio of corresponding perimeters is. the ratio of the base areas, lateral areas, and total areas of the solids is. the ratio of the volumes of the solids is. 7

9 Surface Area and Volume WS1 Prisms and Pyramids Find the lateral area and total surface area for each shape. Draw each shape (or the side shapes) and organize work neatly! 1. Rectangular Prism with sides 4 X 4 X 9 in. 2. Cube with side 3.5 m 3. Right square pyramid with base sides of 18 feet and a height of 12 feet 4. Square prism with the base having sides of 5 cm; prism height of 8 cm 5. Regular square pyramid with base edge 24 and lateral edge Regular triangular pyramid with base edge 4 and slant height 12 (exact value) 7. Right triangular prism with the base triangle having sides of 6.5, 7, and 10.5 and height of 4 to the side of 10.5; height of the prism is Right prism with an isos. triangle base with sides of 13, 13, and 10; height of the prism is 7 9. Regular triangular pyramid with base edge 18 and height Right square pyramid with base edge 14; pyramid height of 7 (exact value) 11. Right prism with equilateral triangle base with sides of 8; ht. of the prism is 13 (exact value) 12. Right trapezoidal prism which has an isosceles trapezoid base with parallel sides of length 6 cm and 12 cm and with legs of length 5 cm; the height of the prism is 10 cm 13. All six edges of a regular triangular pyramid have a length of 4. (exact value) 14. The diagram shows the plans for building a storage shed. If the storage shed is made from aluminum panels, how many square feet of aluminum are needed to build the structure? Consider exterior panels only (not the floor or upper base of the rectangular prism) and round the answer to the nearest tenth. 15. How much material would be needed to cover a pillow of the shape below? All lengths are stated in inches rounded to the nearest tenth of an inch

10 Find the volume of each figure. Round answers to the nearest tenth if necessary. 16. Regular right pentagonal pyramid with side 4 in., and height 15 in. 17. Right triangular prism with right triangle base of sides 6, 8, and 10 m, and a height of 12 m 18. Cube with side length of 6 cm 19. Rectangular prism with sides of 3 in, 4 in, and 15 in. 20. Find the length of a cube with a volume of 2197 in What is the height of a pyramid if it has a volume of 30 units 3 and has a base measuring 5 units by 6 units? 22. 9

12 14. The radius of the Earth is about 7,900 miles. About 70% of the Earth s surface is water. How much of the Earth s surface is land? Round your answer to the nearest million square miles. 15. A roof in the shape of a half-cylinder covers the Center Street Ice Rink. The ice rink is a rectangle having a width of 50 feet and a length of 80 feet. What is the surface area, to the nearest square foot, of the roof? 16. A standard drinking straw is 19.5 cm long and has a diameter of 0.6 cm. How many square centimeters, to the nearest square centimeter, of plastic are needed to make 1,000 straws? 17. The exterior nose cone of the rocket shown is to be painted with a special sealant. How much surface area, to the nearest tenth of a square foot, needs to be covered with sealant? 18. The gel caplet is made to be filled with medicine. If the dimensions indicated are in millimeters, how many square millimeters of the gel coating are needed to make 100 caplets? (nearest sq. mm) 11

13 19. The shapes below represent kids toys that pop the end off. If the dimensions are indicated in centimeters, find the number of square centimeters (exterior surfaces only) that need to be painted for each toy. (nearest tenth) Find the volume of each figure. Round answers to the nearest tenth if necessary; but leave in terms of if possible r = 1.2 ft. 18 in. 6 in. 22. Cylinder with a diameter of 8 cm and a height of 6 cm 23. Sphere with a diameter 16 inches ft. r = 3.2 ft. 26. What is the radius of a cone whose volume is 1500 inches 3 and whose height is 20 inches? 27. What is the height of a cylinder whose base has a circumference of 8 units and whose volume is 144 cubic units? 12

14 28. Find the volume, in terms of x, of a sphere with a diameter of 4x. 29. What is the volume of the largest ball that will fit into a cubical box with edges of 12 inches? (round to the nearest tenth) 30. How many cubic inches of foam filler would fit around the ball placed in the box described in question 17? (nearest cubic inch) 31. Find the volume of the solid in the diagram below, which consists of a square prism with a cylindrical hole cut through the middle. (nearest tenth) 13

15 Surface Area and Volume WS3 Mixed Review Find the total surface area of each figure. If necessary, state the answer in terms of

16 Find the surface area of a cube whose side has a length of 4 cm. 8. Find the surface area of the rectangular prism whose dimensions are 4 x 16 x Find the surface area of a right square prism with a height of 6 inches. The sides of the base measure 2 inches. 10. Find the surface area of a prism whose base is a right triangle with sides of lengths 9 ft, 12 ft, and 15 ft and whose height is 10 feet. 11. Consider a sphere with a radius of 16 cm. If the radius of the sphere is doubled, what happens to the surface area? [Hint: try it!] 12. Find the surface area of a right cone with a radius 5.1 inches, height 2.1 inches, and slant height 5.5 inches. Express your answer in terms of. 13. Find the surface area of a regular square pyramid. The base has an edge of length 12 cm and the slant height is 6 10 cm. (exact value) 14. If the edges of a cube are tripled, what happens to the surface area? [Hint: try it using x as the original side length] 15. A semicircular cylinder is formed by cutting a solid cylinder with a radius of 8 ft. and height of 10 ft. in half along a diameter ( length-wise ). Find the surface area of the semicircular cylinder. (exact value) 16. Find the length of the edge of a cube whose surface area is 294 square units. 15

17 17. Find the height of a right cylinder whose surface area is 4 square units and whose radius is 0.5 units. 18. A rectangular prism has a surface area of 136 square units. If the width of the prism is 4 units and the height is 3 units, what is the length of the prism? 19. Find the volume. 20. Find the volume in terms of. 21. If the surface area of a cube is 216, find the volume of the cube. 22. If the volume of a rectangular prism is expressed as be which of the following: 3 2 x 2x 3x, then the dimensions could (a) x, (x+1), (x+3) (c) x, (x+1), (x-3) (b) (x 2 + 3), (x-1) (d) (x 2 3), (x+1) 23. Which has the same volume as a sphere with radius 6? (a) a cylinder with radius 4 and height 16 (b) a cone with radius 6 and height 24 (c) a cube whose edges are 6 (d) a pyramid with base area 36 u 2 and height If the base edge of a square pyramid is doubled, what will happen to the volume of the pyramid? (a) it will be half (c) it will increase four times (b) it will double (d) it will increase six times 16

18 25. If the circumference of the base of a cylinder is 2 and the height is 1, find the surface area. State the answer in terms of. 26. The height of a cone is 9 cm and the radius of the base is 12 cm. Find the surface area of the cone. State the answer in terms of. Find the surface area and the volume for each figure. State the answer in terms of or in simplest radical form if necessary A regulation baseball must have a circumference between 9 inches and 9.25 inches. Find the range of baseball surface areas. Round your answers to the nearest tenth. 30. What is the height of a cement patio that has a length of 144 inches, a width of 168 inches, and was filled with 96,768 in 3 of cement? 31. What is the volume of the largest ball that will fit into a cubical box whose sides measure 8 inches? State the answer in terms of. 32. If a cylindrical water tank which is 400 cm tall with a diameter of 200 cm is filled with water, how many conical shaped paper cups can be completely filled with water if the cups have a 12 cm diameter and are 20 cm tall? [Assume there is no waste of the water!] 33. One paint roller has length 11 inches and a diameter of 2 inches. A second roller has length 7 inches and a diameter of 3 inches. Which roller can spread more paint in one revolution? How much more paint (nearest tenth of a square inch)? 17

19 Find the surface area and volume for each figure. Leave answers in simplest radical form if necessary square pyramid 36. If the following tank is in the shape of a cylinder with ends that are hemispheres, find the total volume of the tank. State the answer in terms of and then also rounded to the nearest tenth. 18

20 Section 12:5 - Similarity Ratios Practice Perimeter, Area, SA, Vol. 1. A quadrilateral with sides of 8 cm, 9 cm, 6 cm, and 5 cm has area 45 cm 2. Find the area of a similar quadrilateral whose longest side is 15 cm. 2. A pentagon with sides of 3 m, 4 m, 5 m, 6 m, and 7 m has area 48 m 2. Find the perimeter of a similar pentagon whose area is 27 m Two spheres have diameters of 24 cm and 36 cm. Find the ratio of their surface areas and the ratio of their volumes. 4. Two spheres have volumes of 2 and 16 cubic units respectively. Find the ratio of their diameters and the ratio of their surface areas. 5. Two regular octagons have perimeter 16 cm and 32 cm, respectively. What is the ratio of their areas? 6. Two similar polygons have a scale factor 7:5. The area of the large polygon is 147. Find the area of the smaller polygon. 7. Two cones have radii of 6 cm and 9 cm. Their heights are 10 cm and 15 cm respectively. Are the cones similar? Find the ratio of their volumes. 19

21 8. Two similar pyramids have heights of 12 and 18. Find the ratio of their base areas and the ratio of their lateral areas. 9. The areas of two circles are 100 and 36. Find the ratio of their radii and the ratio of their circumferences. 10. Two regular pentagons have sides of 14 m and 3.5 m, respectively. Find their scale factor and the ratio of their areas. 11. The diagonal of one cube has a length of 2 2 cm. A diagonal of another cube is 4 2 cm. The larger cube has a volume of 64 cm 3. Find the volume of the smaller cube. 12. Two similar cones have radii of 4 cm and 6 cm. The total surface area of the smaller cone is 36 cm 2. Find the total surface area of the larger cone. 13. Two triangles are similar. The longest side of one triangle is five times as long as the corresponding side of the second triangle. How many times greater is the area of the larger triangle than the smaller triangle? 14. Two similar triangles have areas of 36 cm 2 and 16 cm 2. If a side of the larger triangle is 12 cm in length, find the length of the corresponding side in the smaller triangle. 15. Two similar cones have volumes of 8 and 27. Find the ratio of their surface areas. 16. Two similar pyramids have volumes of 9 and 729 respectively. Find the ratio of their heights and the ratio of their surface areas. 20

22 17. The area of one equilateral triangle is three times the area of a smaller equilateral triangle with a side of 8 cm. What is the length of a side of the larger triangle? 18. The ratio of the perimeters of two similar triangles is 2:3. If the area of the smaller triangle is 15 m 2, find the area of the larger triangle. 19. The length of each edge of one pyramid is five times the length of each edge of a similar pyramid. Find the ratio of their volumes. 20. The volume of the larger of two similar right rectangular prisms is 480 cm 3. The heights of the prisms are 9 cm and 12 cm, respectively. Find the volume of the smaller prism. 21

23 Chapter 12 Review In #1-10, name the solid. Find the exact surface area and volume in. 3 in. 4 in km 10 km 26 cm 24 cm cm ft. 4 ft ft. 5 m 4 m 6 m 6 m 22

24 m 6 mi. 3 m 10 mi. 6 mi. 9 m 7 m 10 m 8 mi cm 5 cm 5 km 14 km 6 km In #11, find the exact surface area and volume mi. 3 mi. 10 mi. 4 mi. 8 mi. 23

25 12. The surface area of a rectangular prism with length 4 and width 8 is 136 square inches. Find the height of the prism. 13. The volume of a cube is cubic meters. Find the length of a side of the cube. 14. What is the surface area of a cube if the area of one side of the cube is 144 in Find the surface area of a rectangular prism whose dimensions are 4ft. x 6 ft. x 2 ft. 16. A triangular pyramid has a base that is congruent to its lateral faces. The base edge is 24 cm and the slant height is 12 3 cm. What is the surface area of the pyramid?(exact & rounded nearest tenth) 17. The volume of a rectangular prism is 90 cm 3. If the length is 6 cm and the width is 3 cm, find the height of the prism. 18. A square pyramid has a volume of 400 ft 3. If the height is 13 ft, find the measure of a side of the base. (round nearest tenth) 19. Find the volume of a cube with a surface area of 96 m How does doubling the height and radius of a cylinder affect the volume? 21. A volcano has the shape of a cone. The diameter of the base of the volcano is about 9 miles. The height of the volcano is about 1000 feet. What is the approximate volume of the volcano to the nearest cubic mile? (Use 1 mile = 5280 feet) 22. Find the volume of a right triangular prism whose base is an isosceles triangle with legs measuring 4 inches and a base of 6 inches, and whose height is 13 inches. (nearest tenth) 23. A basketball has a radius of approximately 4.75 inches when filled. How much material is needed to make one? How much air will it hold? (nearest tenth) 24. A pile of sand has a circular base that is 8 yards in diameter. If the pile is about how much sand is in the pile? (nearest tenth) yards high, 25. Find the height of a regular pyramid with volume cm 3 and a base area of 44.2 cm 2. Round to the nearest tenth. 24

26 26. The volume of a rectangular pool is 15,360 cubic meters. Its length, width, and depth are in the ratio of 10:6:4. Find the number of meters in each of the three dimensions of the pool. Chapter 12 Review ANSWERS 1. sphere; SA= 144 mm 2 ; V= 288 mm 3 2. cone; SA= 24 in. 2 ; V= 12 in cylinder; SA= 112 km 2 ; V= 160 km 3 4. triangular prism; SA=2280 cm 2, V=6000 cm 3 5. rectangular prism; SA=276 ft. 2, V=280 ft square pyramid; SA=96 m 2, V=48 m 3 7. triangular prism; SA=192 mi. 2, V=144 mi triangular prism; SA=117 m 2, V=63 m 3 9. SA= 57 cm 2 ; V= 63 cm SA= km 2 ; V= km SA=340 mi. 2 ; V=372 mi h = 3 in. 13. s = 7.1 m 14. SA = 864 sq. in sq. ft cm ; cm 17. h = 5 cm 18. S = 9.6 ft 19. V = 64m Volume is multiplied by V = 4 3 mi in 23. SA = in ; V = 448.9in V = yds 25. h = 37.3 cm m, 24m, 16m 25

### Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

### Area of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:

Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of

### Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in

Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in

### SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid

Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.

### Solids. Objective A: Volume of a Solids

Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular

### Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.

Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism

### Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel

### Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

### 12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h

Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h The volume is 108 cm 3. The volume V of a prism is V = Bh, where B is the area of a base and h the

### In Problems #1 - #4, find the surface area and volume of each prism.

Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

### Area of Parallelograms (pages 546 549)

A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

### Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number

### VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

### 10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warm-up

10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres 10.4 Day 1 Warm-up 1. Which identifies the figure? A rectangular pyramid B rectangular prism C cube D square pyramid 3. A polyhedron

### Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:

Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard- Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students

### 2nd Semester Geometry Final Exam Review

Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular

### 10-4 Surface Area of Prisms and Cylinders

: Finding Lateral Areas and Surface Areas of Prisms 2. Find the lateral area and surface area of the right rectangular prism. : Finding Lateral Areas and Surface Areas of Right Cylinders 3. Find the lateral

### B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3

45 Volume Surface area measures the area of the two-dimensional boundary of a threedimensional figure; it is the area of the outside surface of a solid. Volume, on the other hand, is a measure of the space

### SURFACE AREA AND VOLUME

SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has

### Lesson 17 ~ Volume of Prisms

Lesson 17 ~ Volume of Prisms 1. An octagonal swimming pool has a base area of 42 square meters. The pool is 3 feet deep. Find the volume of the pool. 2. A fish aquarium is a rectangular prism. It is 18

### Volume of Spheres. A geometric plane passing through the center of a sphere divides it into. into the Northern Hemisphere and the Southern Hemisphere.

Page 1 of 7 9.6 Surface Area and Volume of Spheres Goal Find surface areas and volumes of spheres. Key Words sphere hemisphere A globe is an example of a sphere. A sphere is the set of all points in space

### Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

### Geometry Notes VOLUME AND SURFACE AREA

Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate

### Practice: Space Figures and Cross Sections Geometry 11-1

Practice: Space Figures and Cross Sections Geometry 11-1 Name: Date: Period: Polyhedron * 3D figure whose surfaces are * each polygon is a. * an is a segment where two faces intersect. * a is a point where

### Unit 1 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Unit 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Convert 8 yd. to inches. a. 24 in. b. 288 in. c. 44 in. d. 96 in. 2. Convert 114 in. to yards,

### SOLID SHAPES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier

Mathematics Revision Guides Solid Shapes Page 1 of 19 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier SOLID SHAPES Version: 2.1 Date: 10-11-2015 Mathematics Revision Guides Solid

### Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

### Calculating Area, Perimeter and Volume

Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly

### Perimeter, Area, and Volume

Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

### Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

### Review for Final - Geometry B

Review for Final - Geometry B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A model is made of a car. The car is 4 meters long and the model is 7 centimeters

### Applications for Triangles

Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given

### 12 Surface Area and Volume

12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids

### 12-2 Surface Areas of Prisms and Cylinders. 1. Find the lateral area of the prism. SOLUTION: ANSWER: in 2

1. Find the lateral area of the prism. 3. The base of the prism is a right triangle with the legs 8 ft and 6 ft long. Use the Pythagorean Theorem to find the length of the hypotenuse of the base. 112.5

### Chapter 4: Area, Perimeter, and Volume. Geometry Assessments

Chapter 4: Area, Perimeter, and Volume Geometry Assessments Area, Perimeter, and Volume Introduction The performance tasks in this chapter focus on applying the properties of triangles and polygons to

### Characteristics of the Four Main Geometrical Figures

Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Santa Monica College COMPASS Geometry Sample Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. 1) 5 yd 6 yd

### FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby

### Finding Volume of Rectangular Prisms

MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of three-dimensional composite shapes.

### MENSURATION. Definition

MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters

### Right Prisms Let s find the surface area of the right prism given in Figure 44.1. Figure 44.1

44 Surface Area The surface area of a space figure is the total area of all the faces of the figure. In this section, we discuss the surface areas of some of the space figures introduced in Section 41.

### 11-4 Areas of Regular Polygons and Composite Figures

1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,

### Pizza! Pizza! Assessment

Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the

### 12 Surface Area and Volume

CHAPTER 12 Surface Area and Volume Chapter Outline 12.1 EXPLORING SOLIDS 12.2 SURFACE AREA OF PRISMS AND CYLINDERS 12.3 SURFACE AREA OF PYRAMIDS AND CONES 12.4 VOLUME OF PRISMS AND CYLINDERS 12.5 VOLUME

### Honors Geometry Final Exam Study Guide

2011-2012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.

### Chapter 8 Geometry We will discuss following concepts in this chapter.

Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

### Perimeter, Area, and Volume

Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the

### Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?

Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane

### PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

### Area Long-Term Memory Review Review 1

Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter

### WEIGHTS AND MEASURES. Linear Measure. 1 Foot12 inches. 1 Yard 3 feet - 36 inches. 1 Rod 5 1/2 yards - 16 1/2 feet

WEIGHTS AND MEASURES Linear Measure 1 Foot12 inches 1 Yard 3 feet - 36 inches 1 Rod 5 1/2 yards - 16 1/2 feet 1 Furlong 40 rods - 220 yards - 660 feet 1 Mile 8 furlongs - 320 rods - 1,760 yards 5,280 feet

### 17.2 Surface Area of Prisms and Cylinders

Name Class Date 17. Surface Area of Prisms and Cylinders Essential Question: How can you find the surface area of a prism or cylinder? Explore G.11.C Apply the formulas for the total and lateral surface

### 3. If AC = 12, CD = 9 and BE = 3, find the area of trapezoid BCDE. (Mathcounts Handbooks)

EXERCISES: Triangles 1 1. The perimeter of an equilateral triangle is units. How many units are in the length 27 of one side? (Mathcounts Competitions) 2. In the figure shown, AC = 4, CE = 5, DE = 3, and

### Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

### The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- Area = 1 2 D x d CIRCLE.

Revision - Areas Chapter 8 Volumes The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- SQUARE RECTANGE RHOMBUS KITE B dd d D D Area = 2 Area = x B

### 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft

2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite

### MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

### The Area is the width times the height: Area = w h

Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what

### Surface Area and Volume Nets to Prisms

Surface Area and Volume Nets to Prisms Michael Fauteux Rosamaria Zapata CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version

### MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume.

MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume For prisms, pyramids, cylinders, and cones: Volume is the area of one base

### 10.1 Areas of Quadrilaterals and triangles

10.1 Areas of Quadrilaterals and triangles BASE AND HEIGHT MUST FORM A RIGHT ANGLE!! Draw the diagram, write the formula and SHOW YOUR WORK! FIND THE AREA OF THE FOLLOWING:. A rectangle with one side of

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

### Scaling Three-Dimensional Figures

exploration Scaling Three-Dimensional Figures A rectangular box can be scaled up by increasing one of its three dimensions. To increase one dimension of the box, multiply the dimension by a scale factor.

### Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

### Chapter 19. Mensuration of Sphere

8 Chapter 19 19.1 Sphere: A sphere is a solid bounded by a closed surface every point of which is equidistant from a fixed point called the centre. Most familiar examples of a sphere are baseball, tennis

### Areas of Rectangles and Parallelograms

CONDENSED LESSON 8.1 Areas of Rectangles and Parallelograms In this lesson you will Review the formula for the area of a rectangle Use the area formula for rectangles to find areas of other shapes Discover

### CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.

TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has

### 8-8 Volume and Surface Area of Composite Figures. Find the volume of the composite figure. Round to the nearest tenth if necessary.

Find the volume of the composite figure. Round to the nearest tenth if necessary. The figure is made up of a triangular prism and a rectangular prism. Volume of triangular prism The figure is made up of

### Fundamentals of Geometry

10A Page 1 10 A Fundamentals of Geometry 1. The perimeter of an object in a plane is the length of its boundary. A circle s perimeter is called its circumference. 2. The area of an object is the amount

### Let s find the volume of this cone. Again we can leave our answer in terms of pi or use 3.14 to approximate the answer.

8.5 Volume of Rounded Objects A basic definition of volume is how much space an object takes up. Since this is a three-dimensional measurement, the unit is usually cubed. For example, we might talk about

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

### b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit

Area is the number of square units that make up the inside of the shape of 1 of any unit is a square with a side length Jan 29-7:58 AM b = base h = height Jan 29-8:31 AM 1 Example 6 in Jan 29-8:33 AM A

### Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

### Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

### Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find

### GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book

GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18

### 12-1 Representations of Three-Dimensional Figures

Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

### S.A. = L.A. + 2B = ph + 2B

Page 1 of 5 View Tutorial 5c Objective: Find the lateral area, total surface area, and volume of rectangular prisms. A prism is a polyhedron with two congruent & parallel bases. The other faces are the

### 2006 Geometry Form A Page 1

2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches

### Filling and Wrapping: Homework Examples from ACE

Filling and Wrapping: Homework Examples from ACE Investigation 1: Building Smart Boxes: Rectangular Prisms, ACE #3 Investigation 2: Polygonal Prisms, ACE #12 Investigation 3: Area and Circumference of

### BLoCK 2 ~ surface AreA And VoLuMe

BLoCK 2 ~ surface AreA And VoLuMe surface area Lesson 10 THree-DiMensionaL FiGUres ------------------------------------------ 52 Lesson 11 DrawinG solids ------------------------------------------------------

### Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object.

Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object. Surface area is the sum of areas of all the faces or sides of a three-dimensional

### Mensuration Introduction

Mensuration Introduction Mensuration is the process of measuring and calculating with measurements. Mensuration deals with the determination of length, area, or volume Measurement Types The basic measurement

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS A solid is a three-dimensional (3D) object, that is, it has length, width and height. One of these dimensions is sometimes called thickness or depth.

### FSA Geometry End-of-Course Review Packet. Modeling and Geometry

FSA Geometry End-of-Course Review Packet Modeling and Geometry MAFS.912.G-MG.1.1 EOC Practice Level 2 Level 3 Level 4 Level 5 uses measures and properties to model and describe a realworld object that

### Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain

AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent

### Signs, Signs, Every Place There Are Signs! Area of Regular Polygons p. 171 Boundary Lines Area of Parallelograms and Triangles p.

C H A P T E R Perimeter and Area Regatta is another word for boat race. In sailing regattas, sailboats compete on courses defined by marks or buoys. These courses often start and end at the same mark,

### Precision and Measurement

NAME DATE PERIOD Precision and Measurement The precision or exactness of a measurement depends on the unit of measure. The precision unit is the smallest unit on a measuring tool. Significant digits include

### Tallahassee Community College PERIMETER

Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides

### Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:

Solid Geometry Solid Geometry is the geometry of three-dimensional space, the kind of space we live in. Three Dimensions It is called three-dimensional or 3D because there are three dimensions: width,

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### Name Date Class. Lateral and Surface Area of a Right Prism. The lateral area of a right prism with base perimeter P and height h is L = Ph.

Name Date Class LESSON 10-4 Reteach Surface Area of Prisms and Cylinders The lateral area of a prism is the sum of the areas of all the lateral faces. A lateral face is not a base. The surface area is

### Surface Area and Volume

1 Area Surface Area and Volume 8 th Grade 10 days by Jackie Gerwitz-Dunn and Linda Kelly 2 What do you want the students to understand at the end of this lesson? The students should be able to distinguish

### GEOMETRY FINAL EXAM REVIEW

GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

### Grade 7/8 Math Circles Winter D Geometry

1 University of Waterloo Faculty of Mathematics Grade 7/8 Math Circles Winter 2013 3D Geometry Introductory Problem Mary s mom bought a box of 60 cookies for Mary to bring to school. Mary decides to bring

### *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review