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GCSE · Geometry and Measures

3.16D Area and Circumference of Circles: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A circle has radius 6 cm. Calculate the circumference of the circle. Give your answer correct to 1 decimal place.

(Total for Question 1 is 2 marks)

A circle has diameter 15 cm. Calculate the circumference of the circle. Give your answer correct to 1 decimal place.

(Total for Question 2 is 2 marks)

A circle has radius 4 cm. Work out the area of the circle. Give your answer correct to 1 decimal place.

(Total for Question 3 is 2 marks)

A circle has diameter 20 cm. Work out the area of the circle. Give your answer correct to the nearest whole number.

(Total for Question 4 is 2 marks)

A circle has radius 3.5 cm. Calculate the circumference of the circle. Give your answer as a multiple of π.

(Total for Question 5 is 1 mark)

A circle has radius 10 cm. Work out the area of the circle. Give your answer as a multiple of π.

(Total for Question 6 is 1 mark)

The area of a circle is 201 cm², correct to 3 significant figures. Work out the radius of the circle. Give your answer correct to 1 decimal place.

(Total for Question 7 is 2 marks)

The circumference of a circle is 69.1 cm, correct to 3 significant figures. Work out the diameter of the circle. Give your answer correct to 1 decimal place.

(Total for Question 8 is 2 marks)

The diagram shows a semicircle with diameter 26 cm. Work out the area of the semicircle. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 9 is 2 marks)

The diagram shows a quarter circle with both straight edges of length 14 cm. Work out the area of the quarter circle. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 10 is 2 marks)

A circle has diameter 9.4 cm. Write down the radius of the circle.

(Total for Question 11 is 1 mark)

A circle has radius 2.5 m. Calculate the circumference of the circle. Give your answer correct to 2 decimal places.

(Total for Question 12 is 2 marks)

A circle has radius 1.2 cm. Work out the area of the circle. Give your answer correct to 2 decimal places.

(Total for Question 13 is 2 marks)

A circle has radius 45 mm. Calculate the circumference of the circle. Give your answer in centimetres, correct to 1 decimal place.

(Total for Question 14 is 2 marks)

The minute hand of a clock has length 9 cm. Work out the distance travelled by the tip of the minute hand in exactly 1 hour. Give your answer correct to 1 decimal place.

(Total for Question 15 is 3 marks)

Dev is fitting safety padding around the edge of a circular trampoline. The circumference of the trampoline is 18.8 m, correct to 3 significant figures. The padding is sold in strips of length 1.2 m, and each strip cannot be cut. Work out the minimum number of strips Dev needs to go all the way around the trampoline.

(Total for Question 16 is 3 marks)

The diagram shows the outline of a running track. It is made from two straight sections, each of length 90 m, and two semicircular ends, each with diameter 60 m. Work out the total distance around one lap of the track. Give your answer correct to the nearest metre.

Diagram NOT accurately drawn

(Total for Question 17 is 4 marks)

Kwame is a workshop technician. He cuts a circular hole of diameter 14 cm from the centre of a square sheet of steel with side length 30 cm, as shown in the diagram. Work out the area of steel remaining. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 18 is 4 marks)

A coin has diameter 2.8 cm.

(a)Calculate the circumference of the coin. Give your answer correct to 1 decimal place.(2)

(b)A collector places 50 identical coins in a row, edge to edge, in a straight line. Work out the total length of the row of coins, in centimetres.(2)

(Total for Question 19 is 4 marks)

Fatima manages a leisure centre. A circular pool cover has radius 4 m. Fatima orders a new, larger cover with its radius increased by 20%. Work out the percentage increase in the area of the cover.

(Total for Question 20 is 4 marks)

Munira is comparing two circular drainpipes. Pipe A has internal diameter 80 mm. Pipe B has internal diameter 100 mm. Munira says, 'Pipe B can carry 25% more water than Pipe A, because its diameter is 25% bigger.' Use calculations to decide whether Munira is correct. You must show your working.

(Total for Question 21 is 5 marks)

Yusuf is painting a circular tabletop with diameter 1.4 m. He needs to apply 2 coats of paint. One litre of paint covers 10 m² for a single coat. Paint is sold in tins of 250 ml, and Yusuf can only buy whole tins. Work out the minimum number of tins Yusuf needs to buy.

(Total for Question 22 is 5 marks)

A circle is drawn inside a square of side length 20 cm so that the circle touches all four sides of the square, as shown in the diagram. Work out the area of the square that is not covered by the circle. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 23 is 4 marks)

A circle has area A cm² and circumference C cm. Given that A = 5C, work out the radius of the circle.

(Total for Question 24 is 3 marks)

Mark scheme · 3.16D Area and Circumference of Circles: Fluency and Exam Drill

Question 1

M1 2 * π * 6 oe (π * 12)
A1 awrt 37.7 (cm)
Answer: 37.7 cm

Question 2

M1 π * 15 oe
A1 awrt 47.1 (cm)
Answer: 47.1 cm

Question 3

M1 π * 4² oe
A1 awrt 50.3 (cm²)
Answer: 50.3 cm²

Question 4

M1 radius = 10 oe (20 / 2), then π * 10²
A1 314 (cm²) cao
Answer: 314 cm²

Question 5

B1 7 π (cm) oe
Answer: 7 π cm (= 22.0 cm to 3 sf)

Question 6

B1 100 π (cm²) oe
Answer: 100 π cm² (= 314.2 cm² to 4 sf)

Question 7

M1 √201 / &π; oe (r² = 201 / π)
A1 awrt 8.0 (cm)
Answer: 8.0 cm

Question 8

M1 69.1 / π oe (d = C / π)
A1 awrt 22.0 (cm)
Answer: 22.0 cm

Question 9

M1 radius = 13 oe (26 / 2), then (π * 13²) / 2
A1 awrt 265.5 (cm²)
Answer: 265.5 cm²

Question 10

M1 (π * 14²) / 4 oe
A1 awrt 153.9 (cm²)
Answer: 153.9 cm²

Question 11

B1 4.7 (cm) cao
Answer: 4.7 cm

Question 12

M1 2 * π * 2.5 oe
A1 awrt 15.71 (m)
Answer: 15.71 m

Question 13

M1 π * 1.2² oe
A1 awrt 4.52 (cm²)
Answer: 4.52 cm²

Question 14

M1 converts 45 mm to 4.5 cm, then 2 * π * 4.5 oe
A1 awrt 28.3 (cm)
Answer: 28.3 cm

Question 15

B1 recognises the tip travels one full circle (the circumference) in 1 hour
M1 2 * π * 9 oe
A1 awrt 56.5 (cm)
Answer: 56.5 cm

Question 16

M1 18.8 / 1.2 oe
A1 awrt 15.7 (strips)
B1 16 (strips), dep on M1, since a partial strip still requires a whole strip (round up, not to the nearest whole number)
Answer: 16 strips

Question 17

M1 2 * 90 oe (= 180, the two straight sections)
M1 π * 60 oe (the two semicircular ends combine to make one full circle of diameter 60 m)
M1 180 + their circle circumference, dep on both M marks
A1 awrt 368 (m)
Answer: 368 m

Question 18

M1 30² oe (= 900, area of the square)
M1 π * 7² oe (= 153.9, area of the circular hole, radius 7)
M1 900 - their circle area, dep on both M marks
A1 awrt 746.1 (cm²)
Answer: 746.1 cm²

Question 19

(a) M1 π * 2.8 oe
(a) A1 awrt 8.8 (cm)
(a) Answer: 8.8 cm
(b) M1 50 * 2.8 oe (uses the diameter, not the circumference, since the coins touch edge to edge along a straight line)
(b) A1 140 (cm) cao
(b) Answer: 140 cm

Question 20

M1 π * 4² oe (= 50.3, original area)
M1 π * 4.8² oe (= 72.4, new area, using new radius = 4 * 1.2 = 4.8)
M1 (their new area - their original area) / their original area * 100 oe, dep on both M marks (or alt method: 1.2² * 100 - 100 oe)
A1 44 (%) cao
Answer: 44%

Question 21

M1 π * 40² oe (= 5026.5, cross-sectional area of Pipe A, radius 40 mm)
M1 π * 50² oe (= 7854.0, cross-sectional area of Pipe B, radius 50 mm)
M1 (their Pipe B area - their Pipe A area) / their Pipe A area * 100 oe, dep on both M marks
A1 awrt 56.3 (%) (or 56.25%) cao
C1 correct conclusion that Munira is incorrect, since the cross-sectional area increases by about 56.25%, not 25%, supported by correct figures
Answer: Munira is incorrect. The cross-sectional area of Pipe B is about 56.25% greater than Pipe A, not 25% greater.

Question 22

M1 π * 0.7² oe (= 1.54, area of the tabletop, radius 0.7 m)
M1 their area * 2 oe (= 3.08 m², area to be covered over 2 coats)
M1 their doubled area / 10 oe (litres of paint needed), dep on both M marks
A1 awrt 0.308 (litres) or awrt 308 (ml)
B1 2 (tins), dep on A1, since 307.88 ml is needed and tins hold 250 ml each, so 1 tin is not enough and Yusuf must round up
Answer: 2 tins

Question 23

M1 recognises that the circle's diameter equals the side of the square, so radius = 10 oe
M1 π * 10² oe (= 314.159, area of the circle)
M1 20² - their circle area, dep on both M marks
A1 awrt 85.8 (cm²)
Answer: 85.8 cm²

Question 24

M1 π * r² = 5 * (2 * π * r) oe, forms the correct equation
M1 divides both sides by π * r (r not equal to 0) to reach r = 10 oe, or equivalent correct simplification
A1 10 (cm) cao (r = 0 rejected since it does not give a circle)
Answer: 10 cm

Area and Circumference of Circles: Fluency and Exam Drill - Worksheets, Questions and Revision

3.16D Area and Circumference of Circles: Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24