5.17F Sector Areas and Arc Lengths: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A circle has radius 7 cm. Work out the circumference of the whole circle. Give your answer to 1 decimal place. Use π = 3.14159.

(Total for Question 1 is 1 mark)

A circle has radius 5 cm. Find the area of the whole circle. Give your answer correct to 1 decimal place. Use π = 3.14159.

(Total for Question 2 is 2 marks)

Find the fraction of the circle represented by a sector with angle 90 degrees. Give the fraction in simplest form and then find the area of the sector for a circle of radius 6 cm. Give your area answer to 1 decimal place. Use π = 3.14159.

(a)Write the fraction of the circle that a 90 degree sector represents, in simplest form.(1)

(b)Find the area of the sector when r = 6 cm. Give your answer to 1 decimal place.(2)

(Total for Question 3 is 3 marks)

A sector has radius 8 cm and angle 45 degrees. Work out the length of the arc of the sector. Give your answer to 1 decimal place. Use π = 3.14159.

(Total for Question 4 is 3 marks)

A wheel has diameter 1.2 m. A tyre maker paints a 60 degree sector on the tyre. Work out the area of the painted sector in square metres. Give your answer to 3 decimal places. Use π = 3.14159.

(Total for Question 5 is 4 marks)

The arc length of a sector is 5 cm and the radius of the circle is 10 cm. Work out the angle of the sector in degrees. Give your answer to 1 decimal place. Use π = 3.14159.

(Total for Question 6 is 4 marks)

A circular garden has radius 14 m. A path is made that follows an arc of 120 degrees around the garden. The path is 2 m wide and runs along the outside edge of the garden (so the outer radius is 16 m). Work out the area of the path only. Give your answer to 1 decimal place. Use π = 3.14159.

(Total for Question 7 is 5 marks)

A circular sign has radius 0.4 m. A coloured sector on the sign has area 0.1005 m². Work out the angle of the coloured sector, in degrees, correct to 1 decimal place. Use π = 3.14159.

(Total for Question 8 is 8 marks)

Mark scheme · 5.17F Sector Areas and Arc Lengths: Foundation Tier Practice

Question 1

B1 43.9823... rounded to 44.0 cm cao
Answer: 44.0 cm

Question 2

M1 use area = π * r² with r = 5
A1 78.5 cm² cao (78.53975... rounded to 78.5)
Answer: 78.5 cm²

Question 3

(a) B1 1/4 cao
(a) Answer: 1/4
(b) M1 area sector = fraction * π * r² = 1/4 * π * 6²
(b) A1 28.3 cm² cao (1/4 * π * 36 = 9*π = 28.27431... -> 28.3)
(b) Answer: 28.3 cm²

Question 4

M1 use arc length = (angle/360) * 2 * π * r = 45/360 * 2 * π * 8
M1 calculate 45/360 = 1/8 so arc length = 1/8 * 2 * π * 8 = 2 * π
A1 6.3 cm cao (2 * 3.14159 = 6.28318 -> 6.3)
Answer: 6.3 cm

Question 5

M1 use r = 0.6 m and area sector = (60/360) * π * r²
M1 substitute: (1/6) * π * 0.6² = (1/6) * π * 0.36
A1 0.188495... m² correct to 3 dp 0.188 m²
B1 final answer stated as 0.188 m² cao
Answer: 0.188 m²

Question 6

M1 use arc = (angle/360) * 2 * π * r so angle = arc * 360 / (2 * π * r)
M1 substitute angle = 5 * 360 / (2 * π * 10) and simplify
A1 28.6 degrees cao (28.6479... -> 28.6 degrees)
B1 final answer given as 28.6 degrees
Answer: 28.6 degrees

Question 7

M1 area path = fraction (120/360) * (π * R² - π * r²)
M1 substitute R = 16, r = 14 so area = 1/3 * π * (256 - 196) = 1/3 * π * 60
M1 calculate 1/3 * 60 = 20 so area = 20 * π
A1 62.8318... -> 62.8 m² (1 dp)
B1 final answer given as 62.8 m² cao
Answer: 62.8 m²

Question 8

M1 use area sector = (angle/360) * π * r²
M1 rearrange to angle = area * 360 / (π * r²)
M1 substitute values: area = 0.1005, r = 0.4 so r² = 0.16
M1 calculate denominator π * r² = 3.14159 * 0.16 = 0.5026544 (or equivalent)
M1 calculate numerator area * 360 = 0.1005 * 360 = 36.18
M1 divide to get angle = 36.18 / 0.5026544 = 72.000... (allow calculator evaluation)
M1 round to 1 decimal place correctly
A1 72.0 degrees cao
Answer: 72.0 degrees

Sector Areas and Arc Lengths: Foundation Tier Practice - Worksheets, Questions and Revision