(a)Write down the mathematical name for the line labelled P.(1)
(b)Write down the mathematical name for the line labelled Q.(1)
(c)Write down the mathematical name for the line labelled R.(1)
(d)Write down the mathematical name for the line labelled S.(1)
(Total for Question 1 is 4 marks)
2
Answer each part below.
(a)The diameter of a circle is 12 cm. Write down the radius of the circle.(1)
(b)The radius of a circle is 4.5 cm. Write down the diameter of the circle.(1)
(Total for Question 2 is 2 marks)
3
Which of these is the correct formula for the circumference of a circle with radius r?
A) π x r
B) π x r2
C) 2 x π x r
D) π x r / 2
(Total for Question 3 is 1 mark)
4
Which of these is the correct formula for the area of a circle with radius r?
A) 2 x π x r
B) π x r2
C) π x r
D) 2 x π x r2
(Total for Question 4 is 1 mark)
5
A circle has radius 4 cm. Work out the circumference of the circle. Give your answer correct to 1 decimal place.
(Total for Question 5 is 2 marks)
6
A circle has diameter 10 cm. Work out the circumference of the circle. Give your answer as a multiple of π.
(Total for Question 6 is 2 marks)
7
A circle has radius 6 cm. Work out the area of the circle. Give your answer correct to 1 decimal place.
(Total for Question 7 is 2 marks)
8
A circle has diameter 14 cm. Work out the area of the circle. Give your answer correct to 1 decimal place.
(Total for Question 8 is 3 marks)
9
Show that the area of a circle with radius 5 cm is 78.5 cm2. Use π = 3.14.
(Total for Question 9 is 2 marks)
10
Grace is edging a circular flower bed with radius 3.5 m. Work out the length of edging she needs. Give your answer correct to 1 decimal place.
(Total for Question 10 is 2 marks)
11
The circumference of a circular table top is 37.68 cm. Use π = 3.14 to work out the diameter of the table top.
(Total for Question 11 is 2 marks)
12
A semicircle has radius 6 cm. Work out the perimeter of the semicircle. Give your answer correct to 1 decimal place.
Diagram NOT accurately drawn
(Total for Question 12 is 3 marks)
13
A semicircle has diameter 20 cm. Work out the area of the semicircle. Give your answer correct to 1 decimal place.
Diagram NOT accurately drawn
(Total for Question 13 is 3 marks)
14
The diagram shows a quarter circle with the two straight edges each of length 8 cm.
Diagram NOT accurately drawn
(a)Work out the area of the quarter circle. Give your answer correct to 1 decimal place.(3)
(b)Work out the perimeter of the quarter circle. Give your answer correct to 1 decimal place.(3)
(Total for Question 14 is 6 marks)
15
Jamal's bicycle wheel has diameter 0.65 m.
(a)Work out the circumference of the wheel. Give your answer correct to 2 decimal places.(2)
(b)The wheel rotates exactly 500 times as Jamal cycles to school. Work out the total distance he travels. Give your answer in metres, correct to the nearest metre.(2)
(Total for Question 15 is 4 marks)
16
A circle has area 78.5 cm2. Use π = 3.14 throughout this question.
(a)Work out the radius of the circle.(3)
(b)Work out the diameter of the circle.(1)
(Total for Question 16 is 4 marks)
17
The diagram shows a shape made from a rectangle measuring 12 cm by 8 cm, with a semicircle of diameter 8 cm attached to one of the 8 cm ends.
Diagram NOT accurately drawn
(a)Work out the perimeter of the shape. Give your answer correct to 1 decimal place.(3)
(b)Work out the area of the shape. Give your answer correct to 1 decimal place.(3)
(Total for Question 17 is 6 marks)
18
Chloe cuts a semicircular notch of diameter 10 cm out of one side of a rectangular sheet of card measuring 16 cm by 10 cm. Work out the area of card remaining. Give your answer correct to 1 decimal place.
Diagram NOT accurately drawn
(Total for Question 18 is 4 marks)
19
Aaliyah makes a washer by cutting a circle of radius 6 cm out of the middle of a circle of radius 10 cm. Work out the area of the shaded washer (ring). Give your answer correct to 1 decimal place.
Diagram NOT accurately drawn
(Total for Question 19 is 4 marks)
20
Priya is choosing between two round pizzas. The small pizza has diameter 24 cm and costs £6.00. The large pizza has diameter 32 cm and costs £9.50. Work out which pizza is better value for money. You must show your working.
(Total for Question 20 is 5 marks)
Mark scheme · 3.16 Area and Circumference of Circles
Question 1
(a) B1 radius oe
(a) Answer: Radius
(b) B1 diameter oe
(b) Answer: Diameter
(c) B1 circumference oe
(c) Answer: Circumference
(d) B1 chord oe
(d) Answer: Chord
Question 2
(a) B1 6 cm cao
(a) Answer: 6 cm
(b) B1 9 cm cao
(b) Answer: 9 cm
Question 3
B1 C oe (2 x π x r)
Answer: C) 2 x π x r
Question 4
B1 B oe (π x r2)
Answer: B) π x r2
Question 5
M1 2 x π x 4 oe (π x 8)
A1 awrt 25.1 (cm)
Answer: 25.1 cm
Question 6
M1 π x 10 oe
A1 10 π cm cao
Answer: 10 π cm (= 31.4 cm to 3 sf)
Question 7
M1 π x 62 oe
A1 awrt 113.1 (cm2)
Answer: 113.1 cm2
Question 8
M1 radius = 7 oe (14 / 2)
M1 π x 72 oe
A1 awrt 153.9 (cm2)
Answer: 153.9 cm2
Question 9
M1 3.14 x 52 oe (3.14 x 25)
A1 78.5 (cm2) cso
Answer: 78.5 cm2 (shown)
Question 10
M1 2 x π x 3.5 oe
A1 awrt 22.0 (m)
Answer: 22.0 m
Question 11
M1 37.68 / 3.14 oe (d = C / π)
A1 12 (cm) cao
Answer: 12 cm
Question 12
M1 π x 6 oe (half the circumference)
M1 + 12 oe (add the diameter)
A1 awrt 30.8 (cm)
Answer: 30.8 cm
Question 13
M1 radius = 10 oe (20 / 2)
M1 π x 102 / 2 oe
A1 awrt 157.1 (cm2)
Answer: 157.1 cm2
Question 14
(a) M1 π x 82 oe
(a) M1 divide by 4 oe
(a) A1 awrt 50.3 (cm2)
(a) Answer: 50.3 cm2
(b) M1 (2 x π x 8) / 4 oe (arc length = π x 8 / 2)
(b) M1 + 16 oe (add the two radii)
(b) A1 awrt 28.6 (cm)
(b) Answer: 28.6 cm
Question 15
(a) M1 π x 0.65 oe
(a) A1 awrt 2.04 (m)
(a) Answer: 2.04 m
(b) M1 500 x their (a) ft, oe 500 x π x 0.65
(b) A1 awrt 1021 (m) ft
(b) Answer: 1021 m
Question 16
(a) M1 78.5 / 3.14 oe (r2 = Area / π)
(a) dM1√25 oe
(a) A1 5 (cm) cao
(a) Answer: 5 cm
(b) B1 10 (cm) ft (double their radius)
(b) Answer: 10 cm
Question 17
(a) M1 12 + 12 + 8 oe (sum of the three straight sides)
(a) M1 + π x 4 oe (semicircle arc, half the circumference of a circle of radius 4)
(a) A1 awrt 44.6 (cm)
(a) Answer: 44.6 cm
(b) M1 12 x 8 oe (rectangle area = 96)
(b) M1 (π x 42) / 2 oe (semicircle area)
(b) A1 awrt 121.1 (cm2)
(b) Answer: 121.1 cm2
Question 18
M1 16 x 10 oe (= 160)
M1 (π x 52) / 2 oe (semicircle area, = 39.27)
dM1 160 - their semicircle area
A1 awrt 120.7 (cm2)
Answer: 120.7 cm2
Question 19
M1 π x 102 oe (= 314.16)
M1 π x 62 oe (= 113.10)
dM1 subtract the two areas
A1 awrt 201.1 (cm2)
Answer: 201.1 cm2
Question 20
M1 π x 122 oe (small pizza area, = 452.4)
M1 π x 162 oe (large pizza area, = 804.2)
M1 finds cost per cm2 (or cm2 per pound) for at least one pizza
A1 both values correct, awrt (e.g. 1.33p and 1.18p per cm2, or 75.4 and 84.7 cm2 per pound)
C1 correct conclusion (large pizza) supported by correct figures
Answer: The large pizza is better value (about 1.18p per cm2 compared with about 1.33p per cm2 for the small pizza).