AREA OF PLANE FIGURES. Volume & area of Solid Structures. BANK PROBATIONARY OFFICER QUANTITATIVE APTITUDE MENSURATION. Circumference of a circle = 2 r
|
|
- Malcolm Burns
- 7 years ago
- Views:
Transcription
1 BANK PROBATIONARY OFFICER QUANTITATIVE APTITUDE MENSURATION AREA OF PLANE FIGURES. Triangle Area of triangle x base x height Area of an equilateral triangle ( side) 4 If the length of the sides of a triangle are a, b and c and if the semiperimeter s ( a b c) then, Area of the triangle s( s a) ( s b)( s c). Parallelogram Area base x height. Rectangle Area Length x Breadth Perimeter Sum of all sides (Length + Breadth) 4. Square Let `a' be the side of square Diagonal a Perimeter 4a 5. Trapezium Area a diagonal Area (sum of parallel sides) x (distance between them) 6. Rhombus Area 7. Circle (Product of the diagonals) Let r be the radius of the circle Area of a circle r, or 4. 7 Circumference of a circle r Length of an Arc r 60 Area of a sector r 60 The unit of area is square metre Volume & area of Solid Structures.. Cuboid Let l, b, and h are respectively the length, breadth and height of a cuboid. Cube Volume of a cuboid lbh Longest diagonal of a cuboid l b h Total surface area (lb+bh+lh) Area of a room (length x breadth) Area of 4 walls of a room (l+b) height Let `a' be the side of a cube Volume of the cube a Longest diagonal x (a Total surface area 6a Total length of all edges a.. Cylinder Volume r h; r - radius of the base Base area r h - height
2 Curved surface area r h Total surface area rh r 4. Pyramid 5. Cone Volume x (area of base) x height If the radius of the base of a cone is r, the height is h and the slant height is l then l h + r Volume r h Area of curved surface rl Total surface area rl + r 6. Sphere Volume 4 r(l + r) r ; r- radius of the sphere Curved surface area 4 r 7. Hemisphere Volume r ; Curved surface area Total surface area r r Volume of spherical shell 4 ( R r ) Volume of a metal in a hollow pipe ( R r ) h; R - external radius Total surface area of an open pipe Rh rh ( R r ) The unit of volume is cubic metre. Solved Examples. Find the area of a right triangle whose hypotenuse is 5 metres and base is metres. Ans: Altitude of the triangle Area of the triangle 5 6 4m. x base x altitude x x 4 6 sq. m.. A lawn is in the form of a rectangle having its sides in the ratio :. The area of the lawn is hectare. Find the length and breadth 6 of the lawn. Ans: Let the length and bread be x and x metres. Then 6x 6 x x Length x 50 50m Breadth x 50 m. A rectangular grassy plot is metres by 78 metres. It has a gravel path.5 metres wide all round it on the inside. Find the area of the path and the cost of constructing it at 7 paise per 000 sq.cm. Ans: Area of path Area of grassy plot - Area of plot excluding the path Rs. ( x x 7) 95 m 7 8 Cost on 000 sq.cm. 7 paise. Total Cost x00 x00 x Rs. 6,
3 D C A B 4. How many bricks will be required for a wall 8m long, 6 m high and.5 cm thick if each brick measures 5 cm by.5 cm by 6 cm? Ans: Volume of wall (800x600x.5) cu.cm Volume of brick (5x.5x6) cu.cm. Number of bricks Volumeof t hew all Volume of abrick 800x600x x5. x6 5. Half cubic metre of gold sheet is extended by hammering so as to cover an area of hectare. Find the thickness of the gold sheet. Ans: Volume of sheet cu.metre x 00x00 x00 cu.cm Area of sheethectare 0,000 sq. metre [0,000x00x00] sq.cm. Thickness Volume Area x00 x00 x00 x0, 000x00 x00 cm cm A rectangular lawn 60 metres by 40 metres has two roads each 5 metres wide, running in the middle of it, one parallel to length and the other parallel to the breadth. Find the cost of gravelling them at 60 paise per square metre. Ans: Area of the road ABCD60x500 sq.m Area of the road EFGH 40x5 00 sq.m. M J E H L K Area of JKLM 5x5 5 sq.m. Area of the path of be gravelled ( ) 475 sq.m. cost of gravelling the path. Rs. Quicker Method 60x475 Rs Area of the road (width of the road) x (length + breadth of the lawn - width of the road) Cost 5( ) 475 sq.m 60x475 Rs A rectangular courtyard.78 metres long and 5.5 metres broad is to be paved exactly with square tiles, all of the same size. What is the largest size of such a tile? Also find the number of tiles? Ans: Largest size of tile H.C.F. of 78 cm and 55 cm cm. Area of courtyard (78x55) sq.cm. Number of tiles 78x55 x The diameter of the driving wheel of a bus is 40 cm. How many revolutions per minute must be the wheel make in order to keep a speed of 66 km. per hour? Ans: Distance covered by wheel in minute 66x000, x00 60 Circumference of wheel,0,000 cms. x x cm. 7 Number of revolutions in minute 0,, F G
4 9. The length of a rectangle is increased by 60%. What per cent should the width be decreased to maintain the same area? Ans: Let the length of rectangle be increased by x%. Then the decrease percentage of breadth to maintain the same area 00 x 00 x In the above problem decrease percentage of 00 breadth % 0. A cube of sides cm. is melted and smaller cubes of sides cm. each are formed. How many such cubes are possible? Ans: Quicker method Required Number Original length of side New length of side 7. Three cubes of metals whose edges are, 4 and 5 cm. respectively are melted and formed into a single cube. If there is no loss of metal in the process, find the side of the new cube. Ans: Quicker method When many cubes integrate into one cube, the side of the new cube is given by side Here, side sum of cubes of sides of all thecubes cm. If the radius of a cylinder is doubled and the height is halved, what is the ratio between the new volume and previous volume? Ans: Let the initial radius and height of the cylinder be r cm and h cm respectively. Then V r h V x r x h r h ( ) New Volume r h Pr evious volume r h Required ratio : PRACTICE TEST. The perimeter of a rectangle is 8 m. and its length is 5m. The breadth of the rectangle is: ) 4 m. ) 6 m ) 8 m. 4) m.. The length of a plot of land is 4 times its breadth. A play ground measuring 00m occupies one third of the total area of the plot. What is the length of the plot, in metres? ) 9 0 ) 8 0 ) 6 0 4) 0. If the width of a rectangle is m. less than its length and its perimeter is m., the area of the rectangle is: ) 4m ) 08m ) 99m 4) 6m 4. The sides of a rectangular park are in the ratio : and its area is 750m. The cost of fencing it at 50 paise per metre is: ) Rs..50 ) Rs. 75 ) Rs ) Rs The least number of equal square slabs that can be fitted in a verandah 0.5m. long and m wide is ) 5 ) 4 ) 4) 6. Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cuboid to that of the sum of
5 the surface area of the cubes. ) 7: 9 ) 6: 5 ) 7: 8 4) 5: 6 7. If the radii of the two sphere are in the ratio :4, what will be the ratio of their volumes? ) : 8 ) : 6 ) : 4 4) : Six spherical copper balls of radius `r' are melted and cast into a cylinderical rod of the metal of same radius. The height of the rod will be ) 4r ) 6r ) 8r 4) r 9. A man walked 0 metres to cross a rectangular field diagonally. If the length of the field is 6 metres, what is the breadth of the field? ) 6 ) 4 ) 4) 8 0. If the ratios of areas of two squares is 9:, the ratio of their perimeter is ) 9: ) : 4 ) : 4) :. If the area of a cirlce is equal to its circumference, then diameter of the circle is: ) cms. ) 4cms. ) cm. 4) cms. If the side of a sqaure is increased by 0%, the area of the square is increased by: ) 4 0 % ) 5 % ) 4 4 % 4) 0 %. If the area of a circle is decreased by 6% then radius of a circle decreases by ) 0 % ) 8 % ) 6 % 4) 6 4 % 4. If the area of a square is increased by 96%, then the side of the square is increased by ) 9 6 % ) 48. 5% ) 4 0 % 4) 4 9 % 5. A rectangular hall 0m. long and 8m. broad, is surrounded by a verandah metres wide. Find the area of the verandah. ) 04m ) 88m ) 96m 4) 0m 6. The surface area of a cube is 600m. The length of its diagonal is: ) 0 0 cm ) cm ) 0 cm 4) 0 cm. 7. Two circular cylinders of equal volume have heights in the ratio :. The ratio of their radii is: ) : ) : ) : 4 4) : 8. A copper sphere of radius cm. is beaten and drawn into a wire of diameter 0.cm. The length of the wire is ) 9m. ) m. ) 8m. 4) 6m. 9. The base of a prism is a triangle of sides m., 4m, and 5m. respectively. The height of the prism is 0m. Then its volume is: ) 60m ) 75m ) 4m 4) 8m 0. One cubic metre of aluminium sheet is extended by hammering, so as to cover the roof with an area 0,000 square metre. The thickness of the sheet is: ) 0.cm. ) 0.0m. ).0cm 4) 0.5cm ANSWERS TO PRACTICE TEST. (). (4). (4) 4. (4) 5. () 6. (a ) 7. (4) 8.() 9. () 0. (). (). (). () 4. () 5. () 6.() 7. () 8. (4) 9. () 0. ()
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 informationVOLUME AND SURFACE AREAS OF SOLIDS
VOLUME AND SURFACE AREAS OF SOLIDS Q.1. Find the total surface area and volume of a rectangular solid (cuboid) measuring 1 m by 50 cm by 0.5 m. 50 1 Ans. Length of cuboid l = 1 m, Breadth of cuboid, b
More informationCHAPTER 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 informationExercise 11.1. Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
11 MENSURATION Exercise 11.1 Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area? (a) Side = 60 m (Given) Perimeter of
More informationSURFACE AREAS AND VOLUMES
CHAPTER 1 SURFACE AREAS AND VOLUMES (A) Main Concepts and Results Cuboid whose length l, breadth b and height h (a) Volume of cuboid lbh (b) Total surface area of cuboid 2 ( lb + bh + hl ) (c) Lateral
More information9 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 informationSandia 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.
More informationSURFACE 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 informationArea 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 informationSolids. 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 informationShape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
More informationChapter 16. Mensuration of Cylinder
335 Chapter 16 16.1 Cylinder: A solid surface generated by a line moving parallel to a fixed line, while its end describes a closed figure in a plane is called a cylinder. A cylinder is the limiting case
More informationArea 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 informationChapter 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
More informationArea 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 informationChapter 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
More informationCSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
More informationWEIGHTS 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
More informationTeacher 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 informationGCSE Exam Questions on Volume Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice.
Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice. Cylindrical glasses of height 10 cm and radius 3 cm are to be filled from the carton. How
More informationThe 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
More informationAngle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees
Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationCHAPTER 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 informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS - SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
More information2006 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
More informationMATHEMATICS 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 informationWednesday 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 information43 Perimeter and Area
43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study
More informationAlgebra 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 informationGAP 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 informationGeometry 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
More informationCIRCUMFERENCE AND AREA OF A CIRCLE
CIRCUMFERENCE AND AREA OF A CIRCLE 1. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take = 3.14) 2. In the given
More informationArea 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
More informationGCSE Revision Notes Mathematics. Volume and Cylinders
GCSE Revision Notes Mathematics Volume and Cylinders irevise.com 2014. All revision notes have been produced by mockness ltd for irevise.com. Email: info@irevise.com Copyrighted material. All rights reserved;
More informationME 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 informationB = 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 informationGeometry Final Exam Review Worksheet
Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please.
More informationSA 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 informationPostulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
More informationGeometry 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
More informationCalculating 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 informationMensuration. The shapes covered are 2-dimensional square circle sector 3-dimensional cube cylinder sphere
Mensuration This a mixed selection of worksheets on a standard mathematical topic. A glance at each will be sufficient to determine its purpose and usefulness in any given situation. These notes are intended
More informationSurface 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 informationPerimeter, 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 informationThe 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 informationALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC
ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC WEEK Calculator paper Each set of questions is followed by solutions so you can check & mark your own work CONTENTS TOPIC
More information12 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
More informationGeometry 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 informationArea 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 information16 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 informationChapter 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
More informationFilling 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
More informationPerimeter, Area and Volume of Regular Shapes
Perimeter, Area and Volume of Regular Sapes Perimeter of Regular Polygons Perimeter means te total lengt of all sides, or distance around te edge of a polygon. For a polygon wit straigt sides tis is te
More informationLesson 9.1 The Theorem of Pythagoras
Lesson 9.1 The Theorem of Pythagoras Give all answers rounded to the nearest 0.1 unit. 1. a. p. a 75 cm 14 cm p 6 7 cm 8 cm 1 cm 4 6 4. rea 9 in 5. Find the area. 6. Find the coordinates of h and the radius
More informationThe 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
More informationThe 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
More informationPerimeter. 14ft. 5ft. 11ft.
Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine
More informationGeometry 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
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical
More information2nd 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
More informationVOLUME 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 informationStudent Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)
Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.
More informationIWCF United Kingdom Branch
IWCF United Kingdom Branch Drilling Calculations Distance Learning Programme Part 2 Areas and Volumes IWCF UK Branch Distance Learning Programme - DRILLING CALCULATIONS Contents Introduction Training objectives
More informationBy the end of this set of exercises, you should be able to:
BASIC GEOMETRIC PROPERTIES By the end of this set of exercises, you should be able to: find the area of a simple composite shape find the volume of a cube or a cuboid find the area and circumference of
More informationFinding 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 information1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?
Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is
More informationLesson 22. Circumference and Area of a Circle. Circumference. Chapter 2: Perimeter, Area & Volume. Radius and Diameter. Name of Lecturer: Mr. J.
Lesson 22 Chapter 2: Perimeter, Area & Volume Circumference and Area of a Circle Circumference The distance around the edge of a circle (or any curvy shape). It is a kind of perimeter. Radius and Diameter
More information2. Complete the table to identify the effect tripling the radius of a cylinder s base has on its volume. Cylinder Height (cm) h
Name: Period: Date: K. Williams ID: A 8th Grade Chapter 14 TEST REVIEW 1. Determine the volume of the cylinder. Use 3.14 for. 2. Complete the table to identify the effect tripling the radius of a cylinder
More informationMATH 100 PRACTICE FINAL EXAM
MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number
More informationUnit 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
More informationArea. Area Overview. Define: Area:
Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.
More information12-1 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
More informationGEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
More information2014 2015 Geometry B Exam Review
Semester Eam Review 014 015 Geometr B Eam Review Notes to the student: This review prepares ou for the semester B Geometr Eam. The eam will cover units 3, 4, and 5 of the Geometr curriculum. The eam consists
More informationArea, Perimeter, Volume and Pythagorean Theorem Assessment
Area, Perimeter, Volume and Pythagorean Theorem Assessment Name: 1. Find the perimeter of a right triangle with legs measuring 10 inches and 24 inches a. 34 inches b. 60 inches c. 120 inches d. 240 inches
More informationGAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement
GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2-D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4
More informationApplications 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
More informationShow 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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationMEASUREMENTS. 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
More informationMULTIPLE 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
More informationFCAT 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 informationPizza! 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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationPERIMETER 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
More informationPractice Test Answer and Alignment Document Mathematics: Geometry Performance Based Assessment - Paper
The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 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, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationSGS4.3 Stage 4 Space & Geometry Part A Activity 2-4
SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4 Exploring triangles Resources required: Each pair students will need: 1 container (eg. a rectangular plastic takeaway container) 5 long pipe cleaners
More information56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
More informationof 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
More informationMCA Formula Review Packet
MCA Formula Review Packet 1 3 4 5 6 7 The MCA-II / BHS Math Plan Page 1 of 15 Copyright 005 by Claude Paradis 8 9 10 1 11 13 14 15 16 17 18 19 0 1 3 4 5 6 7 30 8 9 The MCA-II / BHS Math Plan Page of 15
More informationCCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name:
GPS UNIT 3 Semester 1 NLYTI GEOMETRY Page 1 of 3 ircles and Volumes Name: ate: Understand and apply theorems about circles M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships
More informationArea & Volume. 1. Surface Area to Volume Ratio
1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.
More informationTeeJay Publishers General Homework for Book 3G Ch 9 - circles. Circles
Circles Homework Chapter 9 Exercise 1 1. For each of these circles, say whether the dotted line is a radius or a diameter :- (d) 2. Use two letters to name the line which is a diameter in this circle.
More information1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection?
Student Name: Teacher: Date: District: Description: Miami-Dade County Public Schools Geometry Topic 7: 3-Dimensional Shapes 1. A plane passes through the apex (top point) of a cone and then through its
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More informationCircumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite
More information