Circumference and area of a circle
|
|
|
- James Jackson
- 7 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 penny-farthing 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 right-angled 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
CIRCUMFERENCE 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
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
Postulate 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
Lesson 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
Characteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
Dŵr 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
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
43 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
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
Student 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.
GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book
GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas
Perimeter 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
AREA & 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.
DATE 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
Circumference of a Circle
Circumference of a Circle A circle is a shape with all points the same distance from the center. It is named by the center. The circle to the left is called circle A since the center is at point A. If
Grade 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
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
Geometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
YOU 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
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
Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms.
-NEM-WBAns-CH // : PM Page Areas of Polygons Estimate and measure the area of polygons.. A hockey team chose this logo for their uniforms. A grid is like an area ruler. Each full square on the grid has
Inv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units.
Covering and Surrounding: Homework Examples from ACE Investigation 1: Questions 5, 8, 21 Investigation 2: Questions 6, 7, 11, 27 Investigation 3: Questions 6, 8, 11 Investigation 5: Questions 15, 26 ACE
PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
Math 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
By 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
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
Paper 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
Perimeter. 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
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
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
Mensuration. 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
Calculating 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
CALCULATING THE AREA OF A FLOWER BED AND CALCULATING NUMBER OF PLANTS NEEDED
This resource has been produced as a result of a grant awarded by LSIS. The grant was made available through the Skills for Life Support Programme in 2010. The resource has been developed by (managers
10-4-10 Year 9 mathematics: holiday revision. 2 How many nines are there in fifty-four?
DAY 1 Mental questions 1 Multiply seven by seven. 49 2 How many nines are there in fifty-four? 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
Area is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
GAP 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
Area and Circumference
4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert
Applications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
Developing 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
Objective: To distinguish between degree and radian measure, and to solve problems using both.
CHAPTER 3 LESSON 1 Teacher s Guide Radian Measure AW 3.2 MP 4.1 Objective: To distinguish between degree and radian measure, and to solve problems using both. Prerequisites Define the following concepts.
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
GEOMETRIC 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
Tangent 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
AUTUMN UNIT 3. first half. Perimeter. Centimetres and millimetres. Metres and centimetres. Area. 3D shapes PART 3 MEASURES AND PROPERTIES OF SHAPES
PART AUTUMN first half MEASURES AND PROPERTIES OF SHAPES SECTION Perimeter SECTION Centimetres and millimetres SECTION Metres and centimetres SECTION Key Stage National Strategy CROWN COPYRIGHT 00 Area
All 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
How To Find The Area Of A Shape
9 Areas and Perimeters This is is our next key Geometry unit. In it we will recap some of the concepts we have met before. We will also begin to develop a more algebraic approach to finding areas and perimeters.
Grade 7 Circumference
Grade 7 Circumference 7.SS.1 Demonstrate an understanding of circles by describing the relationships among radius, diameter, and circumference of circles relating circumference to PI determining the sum
Intermediate 2 NATIONAL QUALIFICATIONS. Mathematics Specimen Question Paper 1 (Units 1, 2, 3) Non-calculator Paper [C056/SQP105] Time: 45 minutes
![Intermediate 2 NATIONAL QUALIFICATIONS. Mathematics Specimen Question Paper 1 (Units 1, 2, 3) Non-calculator Paper [C056/SQP105] Time: 45 minutes](/thumbs/40/20949731.jpg "Intermediate 2 NATIONAL QUALIFICATIONS. Mathematics Specimen Question Paper 1 (Units 1, 2, 3) Non-calculator Paper [C056/SQP105] Time: 45 minutes")
[C056/SQP105] Intermediate Time: 45 minutes Mathematics Specimen Question Paper 1 (Units 1,, 3) Non-calculator Paper NATIONAL QUALIFICATIONS 1 Answer as many questions as you can. Full credit will be given
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
Tallahassee Community College PERIMETER
Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides
Lesson 21. Circles. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Circles Objectives Understand the concepts of radius and diameter Determine the circumference of a circle, given the diameter or radius Determine
Mathematics (Project Maths Phase 3)
2014. M328 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2014 Mathematics (Project Maths Phase 3) Paper 2 Ordinary Level Monday 9 June Morning 9:30 12:00 300
Paper 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 2 F Paper Reference(s) 1380/2F Edexcel GCSE Mathematics (Linear) 1380 Paper 2 (Calculator) Foundation Tier Friday 12 November 2010 Morning Time: 1 hour
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
TeeJay 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.
Arc Length and Areas of Sectors
Student Outcomes When students are provided with the angle measure of the arc and the length of the radius of the circle, they understand how to determine the length of an arc and the area of a sector.
Session 7 Circles and Pi (π)
Key Terms in This Session Session 7 Circles and Pi (π) Previously Introduced accuracy area precision scale factor similar figures New in This Session circumference diameter irrational number perimeter
Geometry - Calculating Area and Perimeter
Geometry - Calculating Area and Perimeter In order to complete any of mechanical trades assessments, you will need to memorize certain formulas. These are listed below: (The formulas for circle geometry
8 th Grade Task 2 Rugs
8 th Grade Task 2 Rugs Student Task Core Idea 4 Geometry and Measurement Find perimeters of shapes. Use Pythagorean theorem to find side lengths. Apply appropriate techniques, tools and formulas to determine
You 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:
Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Santa Monica College COMPASS Geometry Sample Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. 1) 5 yd 6 yd
WEDNESDAY, 2 MAY 1.30 PM 2.25 PM. 3 Full credit will be given only where the solution contains appropriate working.
C 500/1/01 NATIONAL QUALIFICATIONS 01 WEDNESDAY, MAY 1.0 PM.5 PM MATHEMATICS STANDARD GRADE Credit Level Paper 1 (Non-calculator) 1 You may NOT use a calculator. Answer as many questions as you can. Full
Circumference CHAPTER. www.ck12.org 1
www.ck12.org 1 CHAPTER 1 Circumference Here you ll learn how to find the distance around, or the circumference of, a circle. What if you were given the radius or diameter of a circle? How could you find
2.3 Circles. instead of. r to avoid the danger of calculating
.3 Circles Note that circumference, diameter, radius, etc. can refer either to the lines themselves ( things ) or to the lengths of those lines; e.g., the length of a radius is often just called the radius.
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
Revision Notes Adult Numeracy Level 2
Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands
How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
Unit 8 Angles, 2D and 3D shapes, perimeter and area
Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest
Area. 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.
Geometry Solve real life and mathematical problems involving angle measure, area, surface area and volume.
Performance Assessment Task Pizza Crusts Grade 7 This task challenges a student to calculate area and perimeters of squares and rectangles and find circumference and area of a circle. Students must find
2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
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
Circumference and Area of a Circle
Overview Math Concepts Materials Students explore how to derive pi (π) as a ratio. Students also study the circumference and area of a circle using formulas. numbers and operations TI-30XS MultiView two-dimensional
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
MCB4UW Optimization Problems Handout 4.6
MCB4UW Optimization Problems Handout 4.6 1. A rectangular field along a straight river is to be divided into smaller fields by one fence parallel to the river and 4 fences perpendicular to the river. Find
Paper 2. Year 9 mathematics test. Calculator allowed. Remember: First name. Last name. Class. Date
Ma KEY STAGE 3 Year 9 mathematics test Tier 6 8 Paper 2 Calculator allowed First name Last name Class Date Please read this page, but do not open your booklet until your teacher tells you to start. Write
CSU 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
Hiker. A hiker sets off at 10am and walks at a steady speed for 2 hours due north, then turns and walks for a further 5 hours due west.
Hiker A hiker sets off at 10am and walks at a steady speed for hours due north, then turns and walks for a further 5 hours due west. If he continues at the same speed, what s the earliest time he could
Calculating the Surface Area of a Cylinder
Calculating the Measurement Calculating The Surface Area of a Cylinder PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping
Exercise Worksheets. Copyright. 2002 Susan D. Phillips
Exercise Worksheets Copyright 00 Susan D. Phillips Contents WHOLE NUMBERS. Adding. Subtracting. Multiplying. Dividing. Order of Operations FRACTIONS. Mixed Numbers. Prime Factorization. Least Common Multiple.
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
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.
The teacher gives the student a ruler, shows her the shape below and asks the student to calculate the shape s area.
Complex area Georgia is able to calculate the area of a complex shape by mentally separating the shape into familiar shapes. She is able to use her knowledge of the formula for the area of a rectangle
2. 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
Wigan LEA Numeracy Centre. Year 3 Mental Arithmetic Test Questions
Wigan LEA Numeracy Centre Year 3 Mental Arithmetic Test Questions Produced by Wigan Numeracy Centre September 000 Test (end of week ) Year 3 Time Block I will read every question twice. In this first set
Lesson 1: Introducing Circles
IRLES N VOLUME Lesson 1: Introducing ircles ommon ore Georgia Performance Standards M9 12.G..1 M9 12.G..2 Essential Questions 1. Why are all circles similar? 2. What are the relationships among inscribed
Numeracy and mathematics Experiences and outcomes
Numeracy and mathematics Experiences and outcomes My learning in mathematics enables me to: develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different
Unit 7 Circles. Vocabulary and Formulas for Circles:
ccelerated G Unit 7 ircles Name & ate Vocabulary and Formulas for ircles: irections: onsider 1) Find the circumference of the circle. to answer the following questions. Exact: pproximate: 2) Find the area
2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
Square Roots and the Pythagorean Theorem
4.8 Square Roots and the Pythagorean Theorem 4.8 OBJECTIVES 1. Find the square root of a perfect square 2. Use the Pythagorean theorem to find the length of a missing side of a right triangle 3. Approximate
What You ll Learn. Why It s Important
What is a circle? Where do you see circles? What do you know about a circle? What might be useful to know about a circle? What You ll Learn Measure the radius, diameter, and circumference of a circle.
Chapter 11. Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem!
Chapter 11 Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem! Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret
Circles: Circumference and Area Lesson Plans
Circles: Circumference and Area Lesson Plans A set of lessons for year 7. Lesson 1: Circumference of the circle and Pi Lesson 2: Area of the circle Lesson 3: Consolidation and Practice Lesson 1: Circumference
Three daily lessons. Year 5
Unit 6 Perimeter, co-ordinates Three daily lessons Year 4 Autumn term Unit Objectives Year 4 Measure and calculate the perimeter of rectangles and other Page 96 simple shapes using standard units. Suggest
Wednesday 13 June 2012 Morning
THIS IS A NEW SPECIFICATION F Wednesday 13 June 2012 Morning GCSE MATHEMATICS B J567/02 Paper 2 (Foundation Tier) *J517120612* Candidates answer on the Question Paper. OCR supplied materials: None Other
Trigonometry LESSON ONE - Degrees and Radians Lesson Notes
210 180 = 7 6 Trigonometry Example 1 Define each term or phrase and draw a sample angle. Angle Definitions a) angle in standard position: Draw a standard position angle,. b) positive and negative angles:
Cylinder Volume Lesson Plan
Cylinder Volume Lesson Plan Concept/principle to be demonstrated: This lesson will demonstrate the relationship between the diameter of a circle and its circumference, and impact on area. The simplest