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KS3 · Geometry and Measures

KS3.M-G11 Circles: Circumference and Area

AQA KS3.M-G11 · Calculators not allowed · about 70 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down the definition of the circumference of a circle.

(1)

State the value of π that you should use in calculations to 2 decimal places.

(1)

A circular plate has radius 10 cm. Calculate its circumference. Give your answer to 1 decimal place.

(2)

A circular pond has diameter 14 m. Work out its area. Give your answer to 1 decimal place.

(2)

Calculate the area of a semicircle with radius 6 cm. Give your answer in terms of π and as a decimal to 1 decimal place.

(2)

A tyre has outer radius 32 cm. A small sticker on the tyre travels once around the tyre. How far does the sticker travel? Give your answer in metres to 1 decimal place.

(2)

A circular flower bed has area 314 cm². Calculate its radius in cm, correct to 1 decimal place. Use π = 3.14.

(2)

Find the circumference of a circle whose area is 50pi cm². Give your answer in terms of π.

(2)

A circular clock face has radius 12 cm. Draw a semicircular arc on the face and shade the semicircle. Calculate the perimeter of the shaded semicircle including the straight edge. Give your answer to 1 decimal place.

(3)

A circular coaster has area 78.5 cm². A smaller circle is cut out from its centre with radius 2 cm. Find the area of the remaining ring, giving your answer to 1 decimal place. Use π = 3.14.

(3)

A circular sign has radius 25 cm. A border of width 3 cm is painted around the outside. Find the area of the painted border. Give your answer to the nearest whole cm². Use π = 3.14.

(3)

A semicircular placemat has diameter 10 cm. Find (a) the area of the semicircle, giving your answer in terms of π, and (b) the perimeter of the semicircle including the straight edge. Give decimal answers to 1 decimal place.

(a)Find the area of the semicircle in terms of π.(1)

(b)Give the area as a decimal to 1 decimal place and find the perimeter including the straight edge to 1 decimal place.(2)

A square of side 8 cm has a quarter-circle of radius 4 cm removed from one corner (the quarter circle sits exactly in the corner). Find the area of the remaining shape. Give your answer to 1 decimal place. Use π = 3.14.

(4)

A circular running track has circumference 157 m. Calculate the radius of the track in metres. Give your answer to 1 decimal place. Use π = 3.14.

(2)

Two identical semicircles each with radius 7 cm are joined along their diameters to make an oval shape. Find the perimeter of this oval to 1 decimal place.

(3)

Find the area of the ring between two concentric circles. The outer radius is 10 cm and the inner radius is 6 cm. Give your answer to 1 decimal place. Use π = 3.14.

(3)

A semicircular window sits on top of a rectangle. The rectangle is 6 m wide and 4 m high. The semicircle has diameter equal to the width of the rectangle. Find the total area of the window to 1 decimal place. Use π = 3.14.

(4)

A school wants to fill a pool formed by a rectangle 20 m long and 8 m wide with a semicircular shallow end whose diameter is the width of the rectangle. The pool will be painted at a cost of 1.80 pounds per square metre. Calculate the total area to be painted and the total cost. Give the area to 1 decimal place and the cost to the nearest penny. Use π = 3.14.

(a)Find the area of the rectangular part of the pool.(1)

(b)Find the area of the semicircular end (diameter 8 m).(1)

(c)Find the total area to be painted and give it to 1 decimal place.(1)

(d)Calculate the total cost to paint the pool at 1.80 pounds per square metre. Give the cost to the nearest penny.(2)

Mark scheme · KS3.M-G11 Circles: Circumference and Area

Question 1

B1 statement that the circumference is the distance around the outside of a circle, oe
Answer: The distance around the outside of a circle

Question 2

B1 π = 3.14 cao
Answer: 3.14

Question 3

M1 use of circumference = 2 x π x r or π x d with r = 10
A1 62.8 cm cao
Answer: 62.8 cm

Question 4

M1 use of area = π x r² with r = 7 m
A1 153.9 m² cao
Answer: 153.9 m²

Question 5

M1 correct method: area semicircle = (1/2) x π x r² with r = 6
A1 18pi cm² and 56.5 cm² cao
Answer: 18pi cm²; 56.5 cm²

Question 6

M1 method: circumference = 2 x π x 32 cm
A1 2.0 m cao
Answer: 2.0 m

Question 7

M1 use of area = π r² and rearrangement r = √area/&π;
A1 10.0 cm cao
Answer: 10.0 cm

Question 8

M1 find r from area = π r² so r² = 50, r = √50
A1 circumference = 2pi r = 2pi √50 = 10pi √2 cm oe
Answer: 10pi √2 cm

Question 9

M1 recognise perimeter = half circumference + diameter = π r + 2r
M1 substitute r = 12 to get π x 12 + 24
A1 61.7 cm cao
Answer: 61.7 cm

Question 10

M1 find area of small circle = π x 2² = 4pi = 12.56 cm² using π = 3.14
M1 subtract from total area: 78.5 - 12.56
A1 65.9 cm² cao
Answer: 65.9 cm²

Question 11

M1 area outer circle with r = 28: π x 28² = 2461.76 approx
M1 area inner circle with r = 25: π x 25² = 1962.5 approx; subtract
A1 499 cm² cao (2461.76 - 1962.5 = 499.26 -> 499 rounded to nearest whole)
Answer: 499 cm²

Question 12

(a) M1 use of area formula for semicircle = (1/2) x π x r² with r = 5
(a) Answer: 12.5pi cm²
(b) M1 convert 12.5pi to decimal using π = 3.14
(b) A1 area = 39.3 cm² and perimeter = 25.7 cm cao
(b) Answer: 39.3 cm²; 25.7 cm

Question 13

M1 find area of square = 8 x 8 = 64 cm²
M1 find area of quarter circle = (π x 4²)/4 = 4pi
M1 subtraction: 64 - 4pi
A1 51.4 cm² cao
Answer: 51.4 cm²

Question 14

M1 use r = circumference / (2pi)
A1 25.0 m cao
Answer: 25.0 m

Question 15

M1 recognise that joining two semicircles along diameters gives full circle circumference
M1 calculate circumference = 2pi r = 2 x 3.14 x 7
A1 44.0 cm cao
Answer: 44.0 cm

Question 16

M1 find outer area = π x 10² = 314.0 and inner area = π x 6² = 113.04
M1 subtract inner from outer
A1 201.0 cm² cao
Answer: 201.0 cm²

Question 17

M1 find area of rectangle = 6 x 4 = 24
M1 find area of semicircle with r = 3: (1/2) x π x 3² = 4.5pi
M1 convert semicircle area to decimal using π = 3.14
A1 38.1 m² cao
Answer: 38.1 m²

Question 18

(a) M1 rectangle area = 20 x 8 = 160 m²
(a) Answer: 160 m²
(b) M1 semicircle area = (1/2) x π x r² with r = 4
(b) Answer: 8pi m²
(c) M1 add rectangle and semicircle areas: 160 + 8pi
(c) Answer: 185.1 m²
(d) M1 multiply area 185.12 by 1.80
(d) A1 £333.22 cao
(d) Answer: £333.22

Circles: Circumference and Area - Worksheets, Questions and Revision