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3.16F Area and Circumference of Circles: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out the circumference of a circle with radius 7 cm. Use π = 3.14.

(Total for Question 1 is 1 mark)

Work out the circumference of a circle with diameter 10 cm. Use π = 3.14.

(Total for Question 2 is 1 mark)

Work out the area of a circle with radius 5 cm. Use π = 3.14.

(Total for Question 3 is 2 marks)

A circular roundabout has diameter 12 m. Work out its area. Use π = 3.14 and give your answer to 1 decimal place.

(Total for Question 4 is 2 marks)

Work out the radius of a circle whose circumference is 18.84 cm. Use π = 3.14 and give your answer to 1 decimal place.

(Total for Question 5 is 2 marks)

A circular flower bed has area 50.24 m². Use π = 3.14. Work out the radius of the flower bed, giving your answer to 2 decimal places.

(Total for Question 6 is 3 marks)

Work out the circumference of a circle with radius 2.5 cm. Use π = 3.14 and give your answer to 2 decimal places.

(Total for Question 7 is 3 marks)

A circular pond has radius 4 m. A path of width 1 m runs all around the pond (the path is a ring around the circle). Work out the area of the path. Use π = 3.14 and give your answer to 1 decimal place.

(Total for Question 8 is 3 marks)

The circumference of a circular track is 62.8 m. Use π = 3.14. Work out the diameter of the track, giving your answer to 1 decimal place.

(Total for Question 9 is 4 marks)

A circular table top has area 153.86 cm². Use π = 3.14. Work out the diameter of the table top, giving your answer to 1 decimal place.

(Total for Question 10 is 4 marks)

A circular sticker has circumference 18.84 cm. Use π = 3.14. Work out the area of the sticker. Give your answer to 2 decimal places.

(Total for Question 11 is 4 marks)

A circular water tank has area 201.06 m². Use π = 3.14.
(a) Work out the radius of the tank to 2 decimal places.
(b) Hence work out the circumference of the tank to 2 decimal places.

(a)(a) Work out the radius of the tank to 2 decimal places.(3)

(b)(b) Hence work out the circumference of the tank to 2 decimal places.(3)

(Total for Question 12 is 6 marks)

Mark scheme · 3.16F Area and Circumference of Circles: Foundation Tier Practice

Question 1

B1 circumference = 2 * π * 7 = 2 * 3.14 * 7 = 43.96 cm; 43.96 or 44.0 awrt
Answer: 43.96 cm (or 44.0 cm awrt 2 sf/1 dp acceptable). The mark scheme accepts 43.96 cao or rounded to 44.0 awrt if a calculator is used and rounding shown explicitly in working (or implied by display).

Question 2

B1 circumference = π * diameter = 3.14 * 10 = 31.4 cm cao
Answer: 31.4 cm

Question 3

M1 use area = π * r², substitution: 3.14 * 5²
A1 78.5 cm² cao
Answer: 78.5 cm²

Question 4

M1 use r = 6 m, area = π * r² = 3.14 * 6²
A1 113.0 m² cao (3.14 * 36 = 113.04 rounds to 113.0 m² to 1 dp)
Answer: 113.0 m²

Question 5

M1 use circumference = 2 * π * r, so r = circumference / (2 * π)
A1 r = 18.84 / (2 * 3.14) = 3.0 cm cao (18.84 / 6.28 = 3.0)
Answer: 3.0 cm

Question 6

M1 use area = π * r² and rearrange: r = √area / &π;
M1 substitute: r = √50.24 / 3.14
A1 r = 4.00 m awrt (50.24 / 3.14 = 16; √16 = 4.00)
Answer: 4.00 m

Question 7

M1 use C = 2 * π * r, substitution: 2 * 3.14 * 2.5
A1 15.7 cm cao (2 * 3.14 * 2.5 = 15.7)
A1 answer to 2 dp 15.70 cm awrt
Answer: 15.70 cm

Question 8

M1 area of outer circle with radius 5 m and inner circle radius 4 m; method: area difference = π * 5² - π * 4²
M1 substitute using 3.14: 3.14 * (25 - 16) = 3.14 * 9
A1 28.3 m² cao (3.14 * 9 = 28.26 rounds to 28.3 to 1 dp)
Answer: 28.3 m²

Question 9

M1 use C = π * d, so d = C / π
M1 substitute: d = 62.8 / 3.14
A1 d = 20.0 m cao (62.8 / 3.14 = 20.0)
B1 final answer given with units m
Answer: 20.0 m

Question 10

M1 use area = π * r², so r² = area / π
M1 substitute: r² = 153.86 / 3.14 = 49.0
A1 r = 7.0 cm cao
A1 diameter = 14.0 cm cao with units
Answer: 14.0 cm

Question 11

M1 find radius from circumference: r = C / (2 * π)
M1 substitute r = 18.84 / (2 * 3.14) = 3.0
M1 use area = π * r² and substitute: 3.14 * 3.0²
A1 area = 28.26 cm² => 28.26 cm² to 2 dp = 28.26 cm² cao
Answer: 28.26 cm²

Question 12

(a) M1 use r = √area / &π;
(a) M1 substitute: r = √201.06 / 3.14
(a) A1 r = 8.00 m awrt (201.06 / 3.14 = 64.03; √64.03 = 8.00 awrt)
(a) Answer: 8.00 m
(b) M1 use C = 2 * π * r with r from part (a)
(b) M1 substitute: C = 2 * 3.14 * 8.00
(b) A1 C = 50.24 m cao (2 * 3.14 * 8 = 50.24)
(b) Answer: 50.24 m

Area and Circumference of Circles: Foundation Tier Practice - Worksheets, Questions and Revision