Circumference and area of a circle


 James Jackson
 1 years ago
 Views:
Transcription
1 c Circumference and area of a circle 22 CHAPTER 22.1 Circumference of a circle The circumference is the special name of the perimeter of a circle, that is, the distance all around it. Measure the circumference and diameter of some circular objects. For each one, work out the value of circ umference. diameter diameter The answer is always just over 3 The value of circ umference is the same for every circle, diameter correct to 3 decimal places. The actual value cannot be found exactly and the Greek letter (pi) is used to represent it. So, for all circles, e c n r e e C f i m r u circ umference diameter and circumference diameter Using C to stand for the circumference of a circle with diameter d, C d and C d To find the circumference of a circle, multiply its diameter by. Example 1 Work out the circumference of a circle with a diameter of 6.8 cm. Give your answer correct to 1 decimal place. Solution Circumference 21.4 cm Multiply the diameter by. Use your calculator s button, if it has one. Otherwise use Round the circumference to 1 decimal place. The units (cm) are the same as the diameter s. 404
2 22.1 Circumference of a circle CHAPTER 22 Sometimes the radius, not the diameter, is given in a question. In that case, one way of finding the circumference is to double the radius to obtain the diameter and then multiply the diameter by. Alternatively, use the fact that a circle s diameter d is twice its radius r, that is, d 2r. Replace d by 2r in the formula C d giving C 2r which can be written as C 2 r Example 2 Work out the circumference of a circle with a radius of 8.2 m. Give your answer correct to 1 decimal place. Solution 2 Method Circumference 51.5 m Method Circumference 51.5 m Double the radius to find the diameter. Multiply the diameter by. Round the circumference to 1 decimal place. The units are m. Substitute 8.2 for r in the formula C 2 r. Round the circumference to 1 decimal place. The units are m. Sometimes the circumference is given and the diameter or radius has to be found. Example 3 The circumference of a circle is 29.4 cm. Work out its diameter. Give your answer correct to 2 decimal places. Solution 3 Method d d 29.4 d Diameter 9.36 cm Substitute 29.4 for C in the formula C d. Divide both sides by. Divide 29.4 by and write down at least four figures of the calculator display. Round the diameter to 2 decimal places. The units are cm. The formula C d can be rearranged with d as the subject and used to find the diameter of a circle, if its circumference is given. Dividing both sides of C d by gives d C To find the diameter of a circle, divide its circumference by. 405
3 CHAPTER 22 Method Diameter 9.36 cm Circumference and area of a circle Divide the circumference by. Round the diameter to 2 decimal places. The units are cm. Exercise 22A If your calculator does not have a button, take the value of to be Give answers correct to 1 decimal place unless stated otherwise. 1 Work out the circumferences of circles with these diameters. a 4.2 cm b 9.7 m c 29 cm d 12.7 cm e 17 m 2 Work out the circumferences of circles with these radii. Give your answers correct to 2 decimal places. a 3.9 cm b 13 cm c 6.3 m d 29 m e 19.4 cm 3 Work out the diameters of circles with these circumferences. a 17 cm b 25 m c 23.8 cm d 32.1 cm e 76.3 m 4 The circumference of a circle is 28.7 cm. Work out its radius. Give your answer correct to 2 decimal places. 5 The diameter of the London Eye is 135 m. Work out its circumference. Give your answer to the nearest metre. 6 The tree with the greatest circumference in the world is a Montezuma cypress tree in Mexico. Its circumference is 35.8 m. Work out its diameter. 7 Taking the Equator as a circle of radius 6370 km, work out the length of the Equator. Give your answer correct to 1 significant figure. 8 The circumference of a football is 70 cm. Work out its radius. 9 A semicircle has a diameter of 25 cm. Work out its perimeter. (Hint: the perimeter includes the diameter.) 10 A semicircle has a radius of 19 m. Work out its perimeter. 25 cm 11 The diagram shows a running track. The ends are semicircles of diameter 57.3 m and the straights are 110 m long. Work out the total perimeter of the track. Give your answer correct to the nearest metre m 19 m 110 m 12 A reel of cotton has a radius of 1.3 cm. The cotton is wrapped round it 500 times. Work out the total length of cotton. Give your answer in metres. 406
4 22.2 Area of a circle CHAPTER The radius of a cylindrical tin of soup is 3.8 cm. Work out the length of the label. (Ignore the overlap.) 14 The diameter of a car wheel is 52 cm. a Work out the circumference of the wheel. Give your answer correct to the nearest centimetre. b Work out the distance the car travels when the wheel makes 400 complete turns. Give your answer in metres. 15 The big wheel of a pennyfarthing bicycle has a radius of 0.75 m. Work out the number of complete turns the big wheel makes when the bicycle travels 1 kilometre Area of a circle The diagram shows a circle which has been split up into equal sectors. The sectors can be rearranged to make this new shape. Splitting the circle up into more and more sectors and rearranging them, the new shape becomes very nearly a rectangle. The length of the rectangle is half the circumference of the circle, and the width of the rectangle is equal to the radius of the circle. The area of the rectangle is equal to the area of the circle. Area of circle 1 2 circumference radius Using A to stand for the area of a circle with radius r, A r r A r 2 radius To find the area of a circle, multiply by the square of the radius. 1 2 circumference This means that the area of a circle is radius radius. 407
5 CHAPTER 22 Circumference and area of a circle Example 4 The radius of a circle is 6.7 cm. Work out its area. Give your answer correct to the nearest whole number. Solution Area 141 cm 2 Press the calculator keys exactly as shown here and then press or press and then press. Round the area to the nearest whole number. The units are cm 2. If the diameter, not the radius, is given, the first step is to halve the diameter to get the radius. Example 5 The diameter of a circle is 9.6 m. Work out its area. Give your answer correct to 1 decimal place. Solution Area 72.4 m 2 Divide the diameter by 2 to get the radius. Square the radius and then multiply by. Round the area to 1 decimal place. The units are m 2. Exercise 22B If your calculator does not have a button, take the value of to be Give answers correct to 3 significant figures. 1 Work out the areas of circles with these radii. a 7.2 cm b 14 m c 1.5 cm d 3.7 m e 2.43 cm 2 Work out the areas of circles with these diameters. a 3.8 cm b 5.9 cm c 18 m d 0.47 m e 7.42 cm 3 The radius of a dartboard is cm. Work out its area to the nearest cm 2. 4 The diameter of Avebury stone circle is 365 m. Work out the area enclosed by the circle. Give your answer correct to 1 significant figure. 408
6 22.3 Circumferences and areas in terms of CHAPTER 22 5 The radius of a semicircle is 2.7 m. Work out its area. 6 The diameter of a semicircle is 8.2 cm. Work out its area. 2.7 m 7 The diagram shows a running track. The ends are semicircles of diameter 57.3 m and the straights are 110 m long. Work out the area enclosed by the track. Give your answer correct to the nearest m m 8.2 cm 110 m 8 The diagram shows a circle of diameter 6 cm inside a square of side 10 cm. a Work out the area of the square. b Work out the area of the circle. c By subtraction, work out the area of the shaded part of the diagram. 9 The diagram shows a circle of radius 7 cm inside a circle of radius 9 cm. Work out the area of the shaded part of the diagram, correct to the nearest cm 2. 6 cm 10 cm 7 cm 9 cm 10 cm 10 The diagram shows an 8 cm by 6 cm rectangle inside a circle of diameter 10 cm. Work out the area of the shaded part of the diagram. 10 cm 6 cm 8 cm 22.3 Circumferences and areas in terms of Answers to questions involving the circumference or area of a circle are sometimes given in terms of,which is exact, not as a number, which is approximate. Example 6 The diameter of a circle is 8 cm. Find the circumference of the circle. Give your answer as a multiple of. Solution 6 8 Circumference 8 cm Multiply the diameter by. Write the 8 before the. The units are cm. 409
7 CHAPTER 22 Circumference and area of a circle Example 7 The radius of a circle is 3 m. Find the area of the circle. Give your answer as a multiple of. Solution Area 9 m 2 Square the radius and then multiply by. Write the 9 before the. The units are m 2. Example 8 The diameter of a semicircle is 12 cm. Find the perimeter of the semicircle. Give your answer in terms of. 12 cm Solution 8 The perimeter is the sum of the arc length and the diameter The arc length is half the circumference of a circle with a diameter of 12 cm. Perimeter 6 12 cm To find the perimeter, add the diameter and the arc length. The units are cm. If the circumference of a circle is given as a multiple of, its diameter can be found. Example 9 The circumference of a circle is 30 m. Find its radius. Solution 9 d Radius 15 m To find the diameter, divide the circumference by. To find the radius, divide the diameter by 2. The units are m. Exercise 22C In Questions 1 4, give the answers as multiples of. 1 Find the circumference of a circle with a diameter of 7 m. 2 Find the area of a circle with a radius of 5 cm Find the circumference of a circle with a radius of 8 cm.
8 Chapter summary CHAPTER 22 4 Find the area of a circle with a diameter of 20 m. 5 The diameter of a semicircle is 18 cm. Find the perimeter of the semicircle. Give your answer in terms of. 6 The radius of a semicircle is 7 cm. Find the perimeter of the semicircle. Give your answer in terms of. 7 The radius of a semicircle is 10 cm. Find its area. Give your answer as a multiple of. 8 The circumference of a circle is 16 cm. Find its diameter. 9 The circumference of a circle is 60 m. Find its radius. 10 The circumference of a circle is 14 cm. Find its area. Give your answer as a multiple of. Chapter summary You should now know: how to find the circumference of a circle using circumference of a circle diameter the formulae C d and C 2 r how to find the diameter (or radius) of a circle if its circumference is known using diameter circum ference or using the formula d C how to find the area of a circle using area of a circle radius radius the formula A r 2 how to solve problems involving the circumference and area of a circle, including compound shapes and shaded areas how to express answers to questions involving the circumference or area of a circle in terms of. Chapter 22 review questions If your calculator does not have a button, take the value of to be Give answers correct to 1 decimal place, unless the question states otherwise. 1 Work out the circumference of a circle with a diameter of 27 cm. 2 Work out the circumference of a circle with a radius of 8.7 m. 3 Work out the diameter of a circle with a circumference of 24.7 cm. 411
9 Circumference and area of a circle CHAPTER 22 4 Work out the radius of a circle with a circumference of 53.2 cm. 5 Work out the area of a circle with a radius of 7.9 m, correct to the nearest m2. 6 Work out the area of a circle with a diameter of 3.2 cm. 7 Stonehenge is surrounded by a circular ditch with a diameter of 104 m. Work out the total distance round the ditch. Give your answer correct to the nearest metre. 8 A discus thrower s circle has a diameter of 2.5 m. Work out the area of the circle. 9 Work out the perimeter of a semicircle with a diameter of 11 cm. 10 Work out the area of a semicircle with a radius of 7.4 m. 11 Find the circumference of a circle with a diameter of 9 cm. Give your answer as a multiple of. 12 Find the area of a circle with a radius of 4 cm. Give your answer as a multiple of. 13 A table has a top in the shape of a circle with a radius of 45 centimetres. a Calculate the area of the circular table top. Give your answer correct to the nearest cm2. The base of the table is also in the shape of a circle. The circumference of this circle is 110 centimetres. b Calculate the diameter of the base of the table. (1384 Nov 1996) 14 The diagram shows a shape, made from a semicircle and a rectangle. The diameter of the semicircle is 12 cm. The length of the rectangle is 14 cm. 14 cm 12 cm Calculate the perimeter of the shape. Give your answer correct to 1 decimal place. (1385 June 2002) 412
10 Chapter 22 review questions CHAPTER A mat is made in the shape of a rectangle with a semicircle added at one end. The width of the mat is 1.52 metres. The length of the mat is 1.86 metres. Calculate the area of the mat. Give your answer in square metres, correct to 2 decimal places m 1.86 m (1385 Nov 1999) 16 The diagram shows a shape. AB is an arc of a circle, centre O. Angle AOB 90. OA OB 6 cm. A 6 cm Calculate a the area b the perimeter of the shape. O 6 cm B 17 The diagram shows a circle of diameter 70 cm inside a square of side 70 cm. Work out the area of the shaded part of the diagram. Give your answer correct to the nearest cm cm 70 cm (1384 Nov 1997) 18 The diagram shows a rightangled triangle ABC and a circle. A, B and C are points on the circumference of the circle. AC is a diameter of the circle. The radius of the circle is 10 cm. AB 16 cm and BC 12 cm. A B 16 cm 12 cm 10 cm 10 cm C Work out the area of the shaded part of the circle. Give your answer correct to the nearest cm 2. (1385 June 1999) 413
11 CHAPTER 22 Circumference and area of a circle 19 4 cm 1 cm Shape A 2 cm 1 cm 2 cm 1 cm 3 cm Shape B 10 cm Diagrams NOT 4 cm a Work out the area of Shape A. b i Work out the perimeter of the semicircle, Shape B. ii Work out the area of the semicircle, Shape B. (1385 June 1998) 20 The diagram shows a rectangle drawn inside a circle. The centre of the circle is at O. The rectangle is 15 cm long and 9 cm wide. Calculate the circumference of the circle. 9 cm O 15 cm (1385 Nov 2001) 21 The diameter of a circle is 12 centimetres. a Work out the circumference of the circle. Give your answer in centimetres correct to one decimal place. 12 cm The length of each diagonal of a square is 20 cm. b Work out the area of the square. (1387 Nov 2004) 414
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 informationWorking 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 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 informationJunior Math Circles November 18, D Geometry II
1 University of Waterloo Faculty of Mathematics Junior Math Circles November 18, 009 D Geometry II Centre for Education in Mathematics and Computing Twodimensional shapes have a perimeter and an area.
More informationDraft 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 information9 Area, Perimeter and Volume
9 Area, Perimeter and Volume 9.1 2D Shapes The following table gives the names of some 2D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right
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 informationNCERT. Area of the circular path formed by two concentric circles of radii. Area of the sector of a circle of radius r with central angle θ =
AREA RELATED TO CIRCLES (A) Main Concepts and Results CHAPTER 11 Perimeters and areas of simple closed figures. Circumference and area of a circle. Area of a circular path (i.e., ring). Sector of a circle
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 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) 111: 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 informationFunctional Skills Mathematics
Functional Skills Mathematics Level Learning Resource Perimeter and Area MSS1/L.7 Contents Perimeter and Circumference MSS1/L.7 Pages 36 Finding the Area of Regular Shapes MSS1/L.7 Page 710 Finding the
More informationPerimeter ABC = a + b + c. 5. Perimeter of parallelogram = 2 x sum of lengths of adjacent sides.
Class 7 ( CBSE ) / Chap 11 /Perimeter & Area. Chapter Facts. 1. Perimeter of a rectangle = 2 (length + breadth) 2. Perimeter of a square = 4 length of its side. Also, side of a square = perimeter 4 3.
More informationName: 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 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 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 informationSolutions Section J: Perimeter and Area
Solutions Section J: Perimeter and Area 1. The 6 by 10 rectangle below has semicircles attached on each end. 6 10 a) Find the perimeter of (the distance around) the figure above. b) Find the area enclosed
More informationLesson 21. Chapter 2: Perimeter, Area & Volume. Lengths and Areas of Rectangles, Triangles and Composite Shapes
ourse: HV Lesson hapter : Perimeter, rea & Volume Lengths and reas of Rectangles, Triangles and omposite Shapes The perimeter of a shape is the total length of its boundary. You can find the perimeter
More informationSOLID 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: 10112015 Mathematics Revision Guides Solid
More informationLESSON 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 informationCONNECT: Areas, Perimeters
CONNECT: Areas, Perimeters 1. AREAS OF PLANE SHAPES A plane figure or shape is a twodimensional, flat shape. Here are 3 plane shapes: All of them have two dimensions that we usually call length and width
More informationAREA. 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 informationnot to be republishe NCERT 12.1 Introduction
AREAS RELATED TO CIRCLES 3 AREAS RELATED TO CIRCLES 1.1 Introduction 1 You are already familiar with some methods of finding perimeters and areas of simple plane figures such as rectangles, squares, parallelograms,
More informationPerimeter and area formulas for common geometric figures:
Lesson 10.1 10.: Perimeter and Area of Common Geometric Figures Focused Learning Target: I will be able to Solve problems involving perimeter and area of common geometric figures. Compute areas of rectangles,
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 informationPERIMETERS AND AREAS
PERIMETERS AND AREAS 1. PERIMETER OF POLYGONS The Perimeter of a polygon is the distance around the outside of the polygon. It is the sum of the lengths of all the sides. Examples: The perimeter of this
More informationCharacteristics 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.
More informationGeometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles
Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.
More information10.1: Areas of Parallelograms and Triangles
10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a
More informationAREA & CIRCUMFERENCE OF CIRCLES
Edexcel GCSE Mathematics (Linear) 1MA0 AREA & CIRCUMFERENCE OF CIRCLES Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser.
More informationDŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet
Dŵr y Felin Comprehensive School Perimeter, Area and Volume Methodology Booklet Perimeter, Area & Volume Perimeters, Area & Volume are key concepts within the Shape & Space aspect of Mathematics. Pupils
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 informationPaper Reference. Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Centre No. Candidate No. Paper Reference 1 3 8 0 4 H Paper Reference(s) 1380/4H Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Higher Tier Friday 11 June 2010 Morning Time: 1 hour 45 minutes
More informationArea LongTerm 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 informationMath 0306 Final Exam Review
Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire
More informationPerimeter of Triangle = Sum of all Sides Perimeter of Triangle = Side + Side + Side
Chapter 11 Perimeter As a present, your parents have bought you a pet, a small puppy for you to play with and take care of. For the first few weeks it is quite content living inside the house with the
More information23. [Perimeter / Area]
3. [Perimeter / rea] Skill 3. Calculating the perimeter of polygons (). MM5. 33 44 MM6. 33 44 Convert all measurements to the same unit. Find and label the length of all sides. dd together all side lengths.
More informationDATE PERIOD. Estimate the product of a decimal and a whole number by rounding the Estimation
A Multiplying Decimals by Whole Numbers (pages 135 138) When you multiply a decimal by a whole number, you can estimate to find where to put the decimal point in the product. You can also place the decimal
More informationGAP CLOSING. 2D Measurement. Intermediate / Senior Student Book
GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas
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 informationI Perimeter, Area, Learning Goals 304
U N I T Perimeter, Area, Greeting cards come in a variety of shapes and sizes. You can buy a greeting card for just about any occasion! Learning Goals measure and calculate perimeter estimate, measure,
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 information10.1 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
More informationCHAPTER 28 THE CIRCLE AND ITS PROPERTIES
CHAPTER 8 THE CIRCLE AND ITS PROPERTIES EXERCISE 118 Page 77 1. Calculate the length of the circumference of a circle of radius 7. cm. Circumference, c = r = (7.) = 45.4 cm. If the diameter of a circle
More informationCircles. The Circle. Drawing Circles. The Annulus. Circles 2. Sectors. Circles 3. List of Contents
Circles List of Contents The Circle Drawing Circles The Annulus Circles 2 Sectors Circles 3 The Circle Relevant formulas are: Circumference of circle = π diameter or C = πd Area of Circle = π radius radius
More informationThe area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2
The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2 s s rectangle: A = l w parallelogram: A = b h h b triangle:
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 informationGrade 7 & 8 Math Circles Circles, Circles, Circles March 19/20, 2013
Faculty of Mathematics Waterloo, Ontario N2L 3G Introduction Grade 7 & 8 Math Circles Circles, Circles, Circles March 9/20, 203 The circle is a very important shape. In fact of all shapes, the circle is
More informationGCSE Mathematics Calculator Foundation Tier Free Practice Set 6 1 hour 30 minutes ANSWERS. Marks shown in brackets for each question (2)
MathsMadeEasy 3 GCSE Mathematics Calculator Foundation Tier Free Practice Set 6 1 hour 30 minutes ANSWERS Marks shown in brackets for each question Typical Grade Boundaries C D E F G 76 60 47 33 20 Legend
More informationPerimeter and Area. Chapter 11 11.1 INTRODUCTION 11.2 SQUARES AND RECTANGLES TRY THESE
PERIMETER AND AREA 205 Perimeter and Area Chapter 11 11.1 INTRODUCTION In Class VI, you have already learnt perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around
More informationPerimeter is the length of the boundary of a two dimensional figure.
Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose
More informationCircle Theorems. Angles at the circumference are equal. The angle in a semicircle is x The angle at the centre. Cyclic Quadrilateral
The angle in a semicircle is 90 0 Angles at the circumference are equal. A B They must come from the same arc. Look out for a diameter. 2x Cyclic Quadrilateral Opposite angles add up to 180 0 A They must
More information6.3A Lesson: How Many Diameters Does it Take to Wrap Around a Circle?*
6.3A Lesson: How Many Diameters Does it Take to Wrap Around a Circle?* Name: Period: Label the center of the circle, C. Draw and label the radius,. Draw and label the diameter,. Term Definition Example
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationGeometry SOL G.11 G.12 Circles Study Guide
Geometry SOL G.11 G.1 Circles Study Guide Name Date Block Circles Review and Study Guide Things to Know Use your notes, homework, checkpoint, and other materials as well as flashcards at quizlet.com (http://quizlet.com/4776937/chapter10circlesflashcardsflashcards/).
More information3. 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
More informationMensuration. The shapes covered are 2dimensional square circle sector 3dimensional 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 informationCHAPTER 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 informationQ1. The grid below is made of rightangled triangles like this: Shade triangles on the grid to make a quadrilateral.
Q1. The grid below is made of rightangled triangles like this: Shade triangles on the grid to make a quadrilateral. Your quadrilateral must have an area of 24 cm 2 and a perimeter of 26 cm. Page 1 of
More informationWorksheets for GCSE Mathematics. Perimeter & Area. mrmathematics.com Maths Resources for Teachers. Shape
Worksheets for GCSE Mathematics Perimeter & Area mrmathematics.com Maths Resources for Teachers Shape Perimeter & Area Worksheets Contents Differentiated Independent Learning Worksheets Perimeter of Shapes
More informationIntegrated 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 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 informationGeometry Non Calculator
Geometry Non Calculator Revision Pack 35 minutes 35 marks To use alongside mymaths.co.uk and livemaths.co.uk to revise for your GCSE exam Page 1 of 14 Q1. Diagram NOT accurately drawn Work out the size
More informationThe 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 informationSupporting your child with maths
Granby Primary School Year 5 & 6 Supporting your child with maths A handbook for year 5 & 6 parents H M Hopps 2016 G r a n b y P r i m a r y S c h o o l 1 P a g e Many parents want to help their children
More informationA = 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 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 2D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4
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 informationEdexcel Mathematics Higher Tier, May 2009 (1380/3H) (Paper 3, noncalculator)
Link to examining board: http://www.edexcel.com/migrationdocuments/qp%20current%20gcse/june%202009/1380_3h_que_20090518.pdf At the time of writing you will be able to download this paper for free from
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 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 informationQ1. Here is a flag. Calculate the area of the shaded cross. Q2. The diagram shows a rightangled triangle inside a circle.
Q1. Here is a flag. Calculate the area of the shaded cross. 2 marks Q2. The diagram shows a rightangled triangle inside a circle. The circle has a radius of 5 centimetres. Calculate the area of the triangle.
More information83 Perimeter and Circumference
Learn to find the perimeter of a polygon and the circumference of a circle. 83 Perimeter Insert Lesson and Title Circumference Here perimeter circumference Vocabulary The distance around a geometric figure
More informationPERIMETER AND AREA OF PLANE FIGURES
PERIMETER AND AREA OF PLANE FIGURES Q.. Find the area of a triangle whose sides are 8 cm, 4 cm and 30 cm. Also, find the length of altitude corresponding to the largest side of the triangle. Ans. Let ABC
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 informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 91.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 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 information10410 Year 9 mathematics: holiday revision. 2 How many nines are there in fiftyfour?
DAY 1 Mental questions 1 Multiply seven by seven. 49 2 How many nines are there in fiftyfour? 54 9 = 6 6 3 What number should you add to negative three to get the answer five? 8 4 Add two point five to
More informationare radii of the same circle. So, they are equal in length. Therefore, DN = 8 cm.
For Exercises 1 4, refer to. 1. Name the circle. The center of the circle is N. So, the circle is 2. Identify each. a. a chord b. a diameter c. a radius a. A chord is a segment with endpoints on the circle.
More informationAll I Ever Wanted to Know About Circles
Parts of the Circle: All I Ever Wanted to Know About Circles 1. 2. 3. Important Circle Vocabulary: CIRCLE the set off all points that are the distance from a given point called the CENTER the given from
More informationMath Tech 1 Unit 11. Perimeter, Circumference and Area. Name Pd
Math Tech 1 Unit 11 Perimeter, Circumference and Area Name Pd 111 Perimeter Perimeter  Units  Ex. 1: Find the perimeter of a rectangle with length 7 m and width 5 m. Ex. 2: Find the perimeter of the
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 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 informationALGEBRA READINESS DIAGNOSTIC TEST PRACTICE
1 ALGEBRA READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the examples, work the problems, then check your answers at the end of each topic. If you don t get the answer given, check your work and
More informationLEFT HAND SIDE = RIGHT HAND SIDE
SIPLE FORULA What is a formula? When you do a calculation, you might add numbers together, subtract numbers, multiply or divide them. Take addition as an example: 7 + 45 = 82 Two given numbers added together
More informationSaturday Xtra XSheet: 12. Revision of Grade 12 Space and Shape Part 1 2D Shapes
Saturday Xtra XSheet: 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 informationGrade 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 informationGEOMETRIC MENSURATION
GEOMETRI MENSURTION Question 1 (**) 8 cm 6 cm θ 6 cm O The figure above shows a circular sector O, subtending an angle of θ radians at its centre O. The radius of the sector is 6 cm and the length of the
More informationDeveloping Conceptual Understanding of Number. Set J: Perimeter and Area
Developing Conceptual Understanding of Number Set J: Perimeter and Area Carole Bilyk cbilyk@gov.mb.ca Wayne Watt wwatt@mts.net Perimeter and Area Vocabulary perimeter area centimetres right angle Notes
More informationCalculating Perimeter
Calculating Perimeter and Area Formulas are equations used to make specific calculations. Common formulas (equations) include: P = 2l + 2w perimeter of a rectangle A = l + w area of a square or rectangle
More informationConics. Find the equation of the parabola which has its vertex at the origin and its focus at point F in the following cases.
Conics 1 Find the equation of the parabola which has its vertex at the origin and its focus at point F in the following cases. a) F(, 0) b) F(0,4) c) F(3,0) d) F(0, 5) In the Cartesian plane, represent
More informationQ1. Lindy has 4 triangles, all the same size. She uses them to make a star. Calculate the perimeter of the star. 2 marks.
Q1. Lindy has 4 triangles, all the same size. She uses them to make a star. Calculate the perimeter of the star. Page 1 of 16 Q2. Liam has two rectangular tiles like this. He makes this L shape. What is
More informationGrade 6 Math Circles March 24/25, 2015 Pythagorean Theorem Solutions
Faculty of Mathematics Waterloo, Ontario NL 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles March 4/5, 015 Pythagorean Theorem Solutions Triangles: They re Alright When They
More informationSan Jose Math Circle February 14, 2009 CIRCLES AND FUNKY AREAS  PART II. Warmup Exercises
San Jose Math Circle February 14, 2009 CIRCLES AND FUNKY AREAS  PART II Warmup Exercises 1. In the diagram below, ABC is equilateral with side length 6. Arcs are drawn centered at the vertices connecting
More informationTangent Properties. Line m is a tangent to circle O. Point T is the point of tangency.
CONDENSED LESSON 6.1 Tangent Properties In this lesson you will Review terms associated with circles Discover how a tangent to a circle and the radius to the point of tangency are related Make a conjecture
More informationArea and Volume 1. Circumference and Area of a Circle. Area of a Trapezium. and Measures. Geometry. Key Point. Key Point.
Geometry and Measures Area and Volume 1 You must be able to: Recall and use the formulae for the circumference and area of a circle Recall and use the formula for the area of a trapezium Recall and use
More information24HourAnswers.com. Online Homework. Focused Exercises for Math SAT. Skill Set 10: Circles
24HourAnswers.com Online Homework Focused Exercises for Math SAT Skill Set 10: Circles Many of the problems in this exercise set came from The College Board, writers of the SAT exam. 1. Which of the following
More informationSection 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 informationName Revision Sheet 1
Name Revision Sheet 1 1 What is 8? Show your working 11 Solve the equation y 1 Round 79 to the nearest 10. 1 Expand ( x 1 0 ) Use BIDMAS to work out 5 1 How many lines of symmetry does a square have? 1
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 informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Edexcel IGCSE Centre Number Mathematics A Paper 3H Monday 6 June 2011 Afternoon Time: 2 hours Candidate Number Higher Tier Paper Reference 4MA0/3H You must have:
More information