Write down the formula for the circumference of a circle in terms of its radius r.
(1)
2
Write down the formula for the area of a circle in terms of its radius r.
(1)
3
A circle has radius 5 cm. Calculate its circumference. Give your answer in terms of π.
(1)
4
A circle has diameter 20 cm. Calculate its area. Give your answer in terms of π.
(1)
5
A circle has radius 9 cm. Calculate its area. Give your answer in terms of π.
(1)
6
A circle has diameter 30 cm. Calculate its circumference. Give your answer in terms of π.
(1)
7
A semicircle has radius 8 cm. Write down, in terms of π, the length of its curved (arc) edge.
(1)
8
Calculate the circumference of a circle with radius 15 cm. Give your answer to 1 decimal place. Use π = 3.14.
(2)
9
Calculate the area of a circle with radius 6 cm. Give your answer to 1 decimal place. Use π = 3.14.
(2)
10
A circular table has diameter 1.4 m. Calculate its circumference. Give your answer to 1 decimal place. Use π = 3.14.
(2)
11
A circular rug has radius 2.5 m. Calculate its area. Give your answer to 1 decimal place. Use π = 3.14.
(2)
12
A circular flower bed has area 200.96 cm2. Calculate its radius. Use π = 3.14.
(2)
13
Find the circumference of a circle whose area is 78.5 cm2. Use π = 3.14.
(2)
14
A circular table has radius 60 cm. A tablecloth overhangs the table by 10 cm all around. Calculate the area of the tablecloth. Use π = 3.14.
(3)
15
A running track's inner edge is a circle of circumference 188.4 m. Calculate the radius of the inner edge. Use π = 3.14. Give your answer in metres.
(3)
16
The area of a circular garden is 1256 m2. Calculate the radius of the garden. Use π = 3.14. Give your answer in metres.
(3)
17
A circular rubber washer has outer radius 12 cm and inner radius 9 cm. Find the area of the ring-shaped washer. Give your answer in terms of π.
(3)
18
A semicircular flower bed has diameter 12 m and sits against a straight wall along its diameter.
(a)Find the area of the flower bed. Give your answer in terms of π.(2)
(b)Find the perimeter of the flower bed, including the straight edge along the wall. Give your answer to 1 decimal place, using π = 3.14.(2)
19
A window is made from a rectangle with a semicircle on top. The rectangle is 8 m wide and 5 m high. The semicircle has diameter equal to the width of the rectangle.
(a)Find the area of the rectangular part.(1)
(b)Find the area of the semicircular part (diameter 8 m). Give your answer to 1 decimal place, using π = 3.14.(2)
(c)Find the total area of the window. Give your answer to 1 decimal place.(2)
Mark scheme · KS3.M-G11D Circles: Circumference and Area: Fluency and Exam Drill
Question 1
B1 C = 2 x π x r oe cao
Answer: C = 2 π r
Question 2
B1 A = π x r2 oe cao
Answer: A = π r2
Question 3
B1 10pi cao
Answer: 10pi cm
Question 4
B1 100pi cao
Answer: 100pi cm2
Question 5
B1 81pi cao
Answer: 81pi cm2
Question 6
B1 30pi cao
Answer: 30pi cm
Question 7
B1 8pi cao
Answer: 8pi cm
Question 8
M1 2 x 3.14 x 15 or equivalent method
A1 94.2 cao
Answer: 94.2 cm
Question 9
M1 3.14 x 62 or equivalent method
A1 113.0 cao
Answer: 113.0 cm2
Question 10
M1 3.14 x 1.4 or equivalent method
A1 4.4 cao
Answer: 4.4 m
Question 11
M1 3.14 x 2.52 or equivalent method
A1 19.6 cao
Answer: 19.6 m2
Question 12
M1 rearrange to r2 = 200.96 / 3.14 = 64
A1 8 cao
Answer: 8 cm
Question 13
M1 find radius from area: r2 = 78.5 / 3.14 = 25, so r = 5
A1 31.4 cao
Answer: 31.4 cm
Question 14
M1 find the tablecloth radius, 60 + 10 = 70
M1 3.14 x 702 or equivalent method
A1 15386 cao
Answer: 15386 cm2
Question 15
M1 rearrange circumference formula to r = C / (2 x π)
M1 substitute 188.4 / 6.28
A1 30 cao
Answer: 30 m
Question 16
M1 rearrange to r2 = A / π
M1 1256 / 3.14 = 400
A1 20 cao
Answer: 20 m
Question 17
M1 outer area = π x 122 = 144pi
M1 inner area = π x 92 = 81pi
A1 63pi cao
Answer: 63pi cm2
Question 18
(a) M1 half x π x 62
(a) A1 18pi cao
(a) Answer: 18pi m2
(b) M1 half circumference + diameter, i.e. (3.14 x 6) + 12
(b) A1 30.8 cao
(b) Answer: 30.8 m
Question 19
(a) B1 40 cao
(a) Answer: 40 m2
(b) M1 half x 3.14 x 42
(b) A1 25.1 cao
(b) Answer: 25.1 m2
(c) M1 add the rectangular and semicircular areas, 40 + 25.12