CONNECT: Volume, Surface Area

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "CONNECT: Volume, Surface Area"

Transcription

1 CONNECT: Volume, Surface Area 2. SURFACE AREAS OF SOLIDS If you need to know more about plane shapes, areas, perimeters, solids or volumes of solids, please refer to CONNECT: Areas, Perimeters 1. AREAS OF PLANE SHAPES; CONNECT: Areas, Perimeters 2. PERIMETERS OF PLANE SHAPES and CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS. You may also need to review Pythagoras Theorem if so, please refer to CONNECT: Pythagoras Theorem The surface area of a 3D shape is the total area of the outside of the shape (De Klerk, 2007, p. 129). So, to work out the surface area of a prism, you need to work out the area of each face and add these areas together. Before we calculate the surface area of an example, have a think about the units we will use to measure surface area. Example: Calculate the surface area of this rectangular prism: If we draw in the edges that are blocked from sight by the other faces, we can see the shapes of all the faces: The faces are all rectangles and so each of their areas is A = l x w units 2. For each of the top and bottom faces, the area is 3cm x 4cm = 12cm 2. For each of the left and right faces, the area is 4cm x 12cm = 48cm 2. For each of the front and back faces, the area is 3cm x 12cm = 36cm 2. So the total surface area is 12 x x x 2 cm 2 that is, 192cm 2. The units are square units because we are measuring area. 1

2 Surface area of a cylinder Take an ordinary A4 sheet of paper. Now roll it into a cylinder so that the edges just meet. Do you realise that you have used a rectangle to make the curved surface of a cylinder? Place your cylinder so that it stands on its circular base. The length of the rectangle is now the circumference of the circle (base) and the width of the rectangle is now the height of the cylinder. (Or vice versa, depending on which way you rolled the cylinder, but that will not make any difference to our formula.) h h l l So the area of the curved surface of the cylinder is A = 2πr h units 2. (2πr is the length of the circumference, which is the same as l, the length of the rectangle.) If the cylinder is open at both ends, the total surface area of the cylinder is just the area of the curved surface. If it is closed at one end, we need to add the area of that circle and if it is closed at both ends, we need to add the area of both circles. So, the total surface area of a cylinder could be any of the following: A = 2πr h units 2 open at both ends OR OR A = 2πr h + πr 2 units 2 open at one end A = 2πr h + 2 πr 2 units 2 closed at both ends. Example: Find the surface area of the closed cylinder over the page. 2

3 r=6cm h=10.3cm We need to use the formula A = 2πr h + 2 πr 2 units 2 cylinder is closed. because the So, A = 2 x π x 6 x x π x 6 2 cm 2 Using a calculator we obtain cm cm 2, that is, approximately Surface Area of a Cone The curved surface area of a cone is a little more involved to calculate. We need to know more than just our usual measurements the radius of the circular base and the perpendicular height of the cone. We also need to know the slant height (s) of the cone. Diagram retrieved January 31, 2013, from 3

4 If we know the slant height of the cone, we can use the formula A = πrs units 2 to find the area of the curved surface. So for an open cone, this formula gives the total surface area of the cone. But if we have a closed cone, we need to add the area of the circle as well. So, the total surface area of a cone will be: A = πrs units 2 open cone A = πrs + πr 2 units 2 closed cone Example: Find the surface area of the following closed cone: s = 8.1cm r = 5.1cm Curved surface area = πrs cm 2 = π x 5.1 x 8.1 cm 2 = cm 2 Area of base = πr 2 cm 2 = π x cm 2 = cm 2 So the total area = cm 2 = cm 2 Round this to approximately 211.5cm 2 4

5 But what if we have a cone and do not know s? For example, find the total surface area of this closed cone: h = 4.1 mm s r = 3.2mm We know the radius and the perpendicular height of the cone, but we need to know the slant height. You can see that the radius, vertical height and slant height form the sides of a right-angled triangle, where the slant height (s) is the hypotenuse. By Pythagoras Theorem, s 2 = r 2 + h 2 s 2 = = To find s, take the square root of 27.05, so = So, s is mm. (To make the final answer as accurate as possible, don t round yet.) Now, the curved surface area = πrs mm 2 = π x 3.2 x mm 2 = mm 2 and the area of the base = πr 2 mm 2 = π mm 2 = mm 2 So the total surface area is mm 2 = mm 2 Only now do we round and so the area is approximately 84.5mm 2 5

6 If you need help with any of the Maths covered in this resource (or any other Maths topics), you can make an appointment with Learning Development through Reception: phone (02) , or Level 3 (top floor), Building 11, or through your campus. REFERENCES De Klerk, J. (2007). Illustrated Maths Dictionary. 4 th ed. Pearson. Melbourne. 6

CONNECT: Volume, Surface Area

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.

More information

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

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

More information

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 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

More information

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

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

More information

Surface Area of Prisms

Surface Area of Prisms Surface Area of Prisms Find the Surface Area for each prism. Show all of your work. Surface Area: The sum of the areas of all the surface (faces) if the threedimensional figure. Rectangular Prism: A prism

More information

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

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

More information

Rugs. This problem gives you the chance to: find perimeters of shapes use Pythagoras Rule. Hank works at a factory that makes rugs.

Rugs. This problem gives you the chance to: find perimeters of shapes use Pythagoras Rule. Hank works at a factory that makes rugs. Rugs This problem gives you the chance to: find perimeters of shapes use Pythagoras Rule Hank works at a factory that makes rugs. The edge of each rug is bound with braid. Hank s job is to cut the correct

More information

Surface Area Quick Review: CH 5

Surface Area Quick Review: CH 5 I hope you had an exceptional Christmas Break.. Now it's time to learn some more math!! :) Surface Area Quick Review: CH 5 Find the surface area of each of these shapes: 8 cm 12 cm 4cm 11 cm 7 cm Find

More information

SURFACE AREA AND VOLUME

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

More information

Chapter 1 Measurement

Chapter 1 Measurement Chapter 1 Measurement Math 1201 1 Chapter 1 Measurement Sections 1.1-1.3: Goals: Converting between imperial units by unit analysis Converting between SI units Converting between SI and imperial units

More information

Line AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint.

Line AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint. Section 8 1 Lines and Angles Point is a specific location in space.. Line is a straight path (infinite number of points). Line Segment is part of a line between TWO points. Ray is part of the line that

More information

Solids. Objective A: Volume of a Solids

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

More information

Draft copy. Circles, cylinders and prisms. Circles

Draft copy. Circles, cylinders and prisms. Circles 12 Circles, cylinders and prisms You are familiar with formulae for area and volume of some plane shapes and solids. In this chapter you will build on what you learnt in Mathematics for Common Entrance

More information

Pythagoras Theorem. Page I can... 1... identify and label right-angled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse

Pythagoras Theorem. Page I can... 1... identify and label right-angled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse Pythagoras Theorem Page I can... 1... identify and label right-angled triangles 2... eplain Pythagoras Theorem 4... calculate the hypotenuse 5... calculate a shorter side 6... determine whether a triangle

More information

Solutions Section J: Perimeter and Area

Solutions Section J: Perimeter and Area Solutions Section J: Perimeter and Area 1. The 6 by 10 rectangle below has semi-circles attached on each end. 6 10 a) Find the perimeter of (the distance around) the figure above. b) Find the area enclosed

More information

Geo - CH10 Practice Test

Geo - CH10 Practice Test Geo - H10 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. lassify the figure. Name the vertices, edges, and base. a. triangular pyramid vertices:,,,,

More information

AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional)

AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) AREA AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) Area is always measured in units 2 The most basic questions that you will see will involve calculating the area of a square

More information

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

Name: Date: Geometry Solid Geometry. Name: Teacher: Pd: Name: Date: Geometry 2012-2013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-7 HW: Pgs: 8-10 DAY 2: SWBAT: Calculate the Volume of

More information

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

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

More information

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

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

More information

Junior Math Circles March 10, D Geometry II

Junior Math Circles March 10, D Geometry II 1 University of Waterloo Faculty of Mathematics Junior Math Circles March 10, 2010 3D Geometry II Centre for Education in Mathematics and Computing Opening Problem Three tennis ball are packed in a cylinder.

More information

Saturday X-tra X-Sheet: 12. Revision of Grade 12 Space and Shape Part 1 2D Shapes

Saturday X-tra X-Sheet: 12. Revision of Grade 12 Space and Shape Part 1 2D Shapes Saturday X-tra X-Sheet: 12 Key Concepts Revision of Grade 12 Space and Shape Part 1 2D Shapes In this session we will focus on summarising what you need to know about: Measurement conversions of units

More information

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. 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

More information

A Resource for Free-standing Mathematics Qualifications

A Resource for Free-standing Mathematics Qualifications When something is measured, the measurement is subject to error. The size of the error depends on the sensitivity of the measuring instrument and how carefully it is used. Often when measurements are given

More information

Section 2.4: Applications and Writing Functions

Section 2.4: Applications and Writing Functions CHAPTER 2 Polynomial and Rational Functions Section 2.4: Applications and Writing Functions Setting up Functions to Solve Applied Problems Maximum or Minimum Value of a Quadratic Function Setting up Functions

More information

*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.

*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle. Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the

More information

Perimeter, Area, and Volume

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

More information

3D Geometry: Chapter Questions

3D Geometry: Chapter Questions 3D Geometry: Chapter Questions 1. What are the similarities and differences between prisms and pyramids? 2. How are polyhedrons named? 3. How do you find the cross-section of 3-Dimensional figures? 4.

More information

The GED math test gives you a page of math formulas that

The GED math test gives you a page of math formulas that Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

More information

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

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.

More information

LESSON SUMMARY. Measuring Shapes

LESSON SUMMARY. Measuring Shapes LESSON SUMMARY CXC CSEC MATHEMATICS UNIT SIX: Measurement Lesson 11 Measuring Shapes Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1 (Some helpful exercises and page numbers are given

More information

Finding Volume of Rectangular Prisms

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.

More information

Module: Mathematical Reasoning

Module: Mathematical Reasoning Module: Mathematical Reasoning Lesson Title: Using Nets for Finding Surface Area Objectives and Standards Students will: Draw and construct nets for 3-D objects. Determine the surface area of rectangular

More information

Section 2.1 Rectangular Coordinate Systems

Section 2.1 Rectangular Coordinate Systems P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is

More information

Measurement of Regular Shapes

Measurement of Regular Shapes Measurement of Regular Shapes Workbook Junior Certificate School Programme Support Service Contents Chapter 1 Perimeter and Area of Squares Page 3 Chapter 2 Perimeter and Area of Rectangles Page 6 Chapter

More information

Fundamentals of Geometry

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

More information

Algebra Geometry Glossary. 90 angle

Algebra Geometry Glossary. 90 angle lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

More information

Engineering Drawing. Anup Ghosh. September 12, Department of Aerospace Engineering Indian Institute of Technology Kharagpur

Engineering Drawing. Anup Ghosh. September 12, Department of Aerospace Engineering Indian Institute of Technology Kharagpur Department of Aerospace Engineering Indian Institute of Technology Kharagpur September 12, 2011 Example -1 1 A vertical square prism (50mm side) 2 A horizontal square prism (35mm side) with axis to VP

More information

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

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

More information

Topic 9: Surface Area

Topic 9: Surface Area Topic 9: Surface Area for use after Covering and Surrounding (Investigation 5) Jillian is wrapping a box of model cars for her brother s birthday. Jillian needs to measure the box to see if she has enough

More information

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 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

More information

Geometry Notes PERIMETER AND AREA

Geometry Notes PERIMETER AND AREA Perimeter and Area Page 1 of 17 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

More information

The formula for the area of a parallelogram is: A = bh, where b is the length of the base and h is the length of the height.

The formula for the area of a parallelogram is: A = bh, where b is the length of the base and h is the length of the height. The formula for the area of a parallelogram is: A = h, where is the length of the ase and h is the length of the height. The formula for the area of a parallelogram is: A = h, where is the length of the

More information

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

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

More information

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

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

More information

Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square. Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional

More information

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3 Geometry Concepts Figures that lie in a plane are called plane figures. These are all plane figures. Polygon No. of Sides Drawing Triangle 3 A polygon is a plane closed figure determined by three or more

More information

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

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.

More information

11-1. Space Figures and Cross Sections. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

11-1. Space Figures and Cross Sections. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary 11-1 Space Figures and Cross Sections Vocabulary Review Complete each statement with the correct word from the list. edge edges vertex vertices 1. A(n) 9 is a segment that is formed by the intersections

More information

Lesson 7: Using Formulas

Lesson 7: Using Formulas Lesson 7: Using Formulas Steps for Solving Problems Using a Formula 1. 2. 3. 4. Example 1 Using the formula: Density = mass/volume or D = m/v Find the density of a rock that has a volume of 20 ml with

More information

CONNECT: Areas, Perimeters

CONNECT: Areas, Perimeters CONNECT: Areas, Perimeters 1. AREAS OF PLANE SHAPES A plane figure or shape is a two-dimensional, flat shape. Here are 3 plane shapes: All of them have two dimensions that we usually call length and width

More information

Worksheets for GCSE Mathematics. Perimeter & Area. mr-mathematics.com Maths Resources for Teachers. Shape

Worksheets for GCSE Mathematics. Perimeter & Area. mr-mathematics.com Maths Resources for Teachers. Shape Worksheets for GCSE Mathematics Perimeter & Area mr-mathematics.com Maths Resources for Teachers Shape Perimeter & Area Worksheets Contents Differentiated Independent Learning Worksheets Perimeter of Shapes

More information

Area of Parallelograms (pages 546 549)

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

More information

A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height

A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side

More information

Week #15 - Word Problems & Differential Equations Section 8.1

Week #15 - Word Problems & Differential Equations Section 8.1 Week #15 - Word Problems & Differential Equations Section 8.1 From Calculus, Single Variable by Hughes-Hallett, Gleason, McCallum et. al. Copyright 25 by John Wiley & Sons, Inc. This material is used by

More information

EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 2. Chapter 5. Working with shape and space

EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 2. Chapter 5. Working with shape and space EDEXCEL FUNCTIONAL SKILLS PILOT Maths Level 2 Chapter 5 Working with shape and space SECTION H 1 Perimeter 75 2 Area 77 3 Volume 79 4 2-D Representations of 3-D Objects 81 5 Remember what you have learned

More information

ME 111: Engineering Drawing

ME 111: Engineering Drawing ME 111: Engineering Drawing Lecture # 14 (10/10/2011) Development of Surfaces http://www.iitg.ernet.in/arindam.dey/me111.htm http://www.iitg.ernet.in/rkbc/me111.htm http://shilloi.iitg.ernet.in/~psr/ Indian

More information

16 Circles and Cylinders

16 Circles and Cylinders 16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two

More information

Name: Perimeter and area November 18, 2013

Name: Perimeter and area November 18, 2013 1. How many differently shaped rectangles with whole number sides could have an area of 360? 5. If a rectangle s length and width are both doubled, by what percent is the rectangle s area increased? 2.

More information

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

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

More information

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

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

More information

12-8 Congruent and Similar Solids

12-8 Congruent and Similar Solids Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. 3. Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio

More information

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 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

More information

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

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

More information

Pizza! Pizza! Assessment

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

More information

CHAPTER 27 AREAS OF COMMON SHAPES

CHAPTER 27 AREAS OF COMMON SHAPES EXERCISE 113 Page 65 CHAPTER 7 AREAS OF COMMON SHAPES 1. Find the angles p and q in the diagram below: p = 180 75 = 105 (interior opposite angles of a parallelogram are equal) q = 180 105 0 = 35. Find

More information

CONNECT: Algebra. 3x = 20 5 REARRANGING FORMULAE

CONNECT: Algebra. 3x = 20 5 REARRANGING FORMULAE CONNECT: Algebra REARRANGING FORMULAE Before you read this resource, you need to be familiar with how to solve equations. If you are not sure of the techniques involved in that topic, please refer to CONNECT:

More information

10-4 Surface Area of Prisms and Cylinders

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

More information

b 2 + h 2 = x 2 b 2 + b 2 = x = x = x 2 x = 10.

b 2 + h 2 = x 2 b 2 + b 2 = x = x = x 2 x = 10. MATH 34A PROBLEM SOLVING SKILLS SOLUTIONS **It is possible that I made some mistakes when writing up these solutions. (Your brain doesn't function as well when you have to type math...) If you catch anything

More information

AREA AND PERIMETER OF COMPLEX PLANE FIGURES

AREA AND PERIMETER OF COMPLEX PLANE FIGURES AREA AND PERIMETER OF OMPLEX PLANE FIGURES AREA AND PERIMETER OF POLYGONAL FIGURES DISSETION PRINIPLE: Every polygon can be dissected (or broken up) into triangles (or rectangles), which have no interior

More information

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 4 AREAS AND VOLUMES This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.

More information

Grade 7/8 Math Circles Winter D Geometry

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

More information

Geometry and Measurement

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

More information

3 Pythagoras' Theorem

3 Pythagoras' Theorem 3 Pythagoras' Theorem 3.1 Pythagoras' Theorem Pythagoras' Theorem relates the length of the hypotenuse of a right-angled triangle to the lengths of the other two sides. Hypotenuse The hypotenuse is always

More information

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

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

More information

28. [Area / Volume] cm 2. in = =

28. [Area / Volume] cm 2. in = = 8. [ / Volume] Skill 8. Calculating the area of polygons by counting squares and triangles on a square grid (). Count the number of fully shaded squares on the grid. If necessary add on the number of half

More information

12-8 Congruent and Similar Solids

12-8 Congruent and Similar Solids Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. Ratio of radii: Ratio of heights: The ratios of the corresponding measures are

More information

Working in 2 & 3 dimensions Revision Guide

Working in 2 & 3 dimensions Revision Guide Tips for Revising Working in 2 & 3 dimensions Make sure you know what you will be tested on. The main topics are listed below. The examples show you what to do. List the topics and plan a revision timetable.

More information

TERMINOLOGY Area: the two dimensional space inside the boundary of a flat object. It is measured in square units.

TERMINOLOGY Area: the two dimensional space inside the boundary of a flat object. It is measured in square units. SESSION 14: MEASUREMENT KEY CONCEPTS: Surface Area of right prisms, cylinders, spheres, right pyramids and right cones Volume of right prisms, cylinders, spheres, right pyramids and right cones the effect

More information

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism.

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. Find the volume of each prism. 3. the oblique rectangular prism shown at the right 1. The volume V of a prism is V = Bh, where B is the area of a base and h is the height of the prism. If two solids have

More information

Grade 7/8 Math Circles Winter D Geometry

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

More information

Calculating Area, Perimeter and Volume

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

More information

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

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:

More information

Area Long-Term Memory Review Review 1

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

More information

Name: Class: Date: Geometry Chapter 3 Review

Name: Class: Date: Geometry Chapter 3 Review Name: Class: Date: ID: A Geometry Chapter 3 Review. 1. The area of a rectangular field is 6800 square meters. If the width of the field is 80 meters, what is the perimeter of the field? Draw a diagram

More information

MENSURATION. Definition

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

More information

9 Area, Perimeter and Volume

9 Area, Perimeter and Volume 9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right

More information

Integrated Algebra: Geometry

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

More information

12-6 Surface Area and Volumes of Spheres. Find the surface area of each sphere or hemisphere. Round to the nearest tenth. SOLUTION: ANSWER: 1017.

12-6 Surface Area and Volumes of Spheres. Find the surface area of each sphere or hemisphere. Round to the nearest tenth. SOLUTION: ANSWER: 1017. Find the surface area of each sphere or hemisphere. Round to the nearest tenth. 3. sphere: area of great circle = 36π yd 2 We know that the area of a great circle is r.. Find 1. Now find the surface area.

More information

Incoming Frederick Douglass HS Geometry Students

Incoming Frederick Douglass HS Geometry Students Incoming Frederick Douglass HS Geometry Students 2016-2017 Dear FDHS Student, To better prepare you for the upcoming school year, it is the expectation is that all students bring the completed assignment

More information

KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number

KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number 1.1 Calculations 1.2 Decimal Numbers 1.3 Place Value Use priority of operations with positive and negative numbers. Simplify

More information

Finding Areas of Shapes

Finding Areas of Shapes Baking Math Learning Centre Finding Areas of Shapes Bakers often need to know the area of a shape in order to plan their work. A few formulas are required to find area. First, some vocabulary: Diameter

More information

17.2 Surface Area of Prisms and Cylinders

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

More information

Wednesday 15 January 2014 Morning Time: 2 hours

Wednesday 15 January 2014 Morning Time: 2 hours Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Wednesday 15 January 2014 Morning Time: 2 hours Candidate Number

More information

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change

More information

Most classrooms are built in the shape of a rectangular prism. You will probably find yourself inside a polyhedron at school!

Most classrooms are built in the shape of a rectangular prism. You will probably find yourself inside a polyhedron at school! 3 D OBJECTS Properties of 3 D Objects A 3 Dimensional object (3 D) is a solid object that has 3 dimensions, i.e. length, width and height. They take up space. For example, a box has three dimensions, i.e.

More information

(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units

(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units 1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units

More information

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.

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

More information

Grade 11 Essential Mathematics Unit 6: Measurement and Geometry

Grade 11 Essential Mathematics Unit 6: Measurement and Geometry Grade 11 Essential Mathematics Unit 6: INTRODUCTION When people first began to take measurements, they would use parts of the hands and arms. For example, a digit was the width of a thumb. This kind of

More information

Geometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam.

Geometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam. Geometry Review Here are some formulas and concepts that you will need to review before working on the practice eam. Triangles o Perimeter or the distance around the triangle is found by adding all of

More information