Perimeter, area and volume · Ages 11–12

Areas of semicircles, rings and shapes made with them worksheet

Part of: Circumference and area of a circle

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Perimeter, area and volume · Ages 11–12

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Find the area of this quarter circle. (Take π as 3.14.) The answer is cm²
Answer:
2.Find the area of this semicircle. (Take π as 3.14.) The answer is cm²
Answer:
3.The shape is a rectangle and a semicircle. Find its area. (Take π as 3.14.) The answer is cm²
Answer:
4.Find the area of the ring (the shaded part). (Take π as 3.14.) The answer is cm²
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5.The square's side equals the quarter circle's radius. Find the shaded area. (Take π as 3.14.) The answer is cm²
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6.Take π as 3.14. A circle of radius 6 cm is cut into many equal slices and laid out as an almost-rectangle. About how long is the rectangle, in cm?
- A. 6
- B. 37.68
- C. 18.84
- D. 12
Choose the right answer
Answer:
7.Take π as 3.14. A circle of radius 15 cm is cut into many equal slices and laid out as an almost-rectangle. About how long is the rectangle, in cm?
- A. 47.1
- B. 30
- C. 15
- D. 94.2
Choose the right answer
Answer:
8.Take π as 3.14. A circle of radius 10 cm is cut into many equal slices and laid out as an almost-rectangle. About how long is the rectangle, in cm?
- A. 31.4
- B. 10
- C. 62.8
- D. 20
Choose the right answer
Answer:
9.A semicircle with a diameter of 6 cm has an area of 14.13 cm². (Take π as 3.14.)
True or false?
Answer:
10.A semicircle with a diameter of 8 cm has an area of 25.12 cm². (Take π as 3.14.)
True or false?
Answer:
11.A semicircle with a diameter of 14 cm has an area of 307.72 cm². (Take π as 3.14.)
True or false?
Answer:
12.A semicircle with a diameter of 4 cm has an area of 6.28 cm². (Take π as 3.14.)
True or false?
Answer:

13.Take π as 3.14. A round pizza 40 cm across is cut into 8 equal slices. What is the area of each slice, in cm²?
Working:
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14.Take π as 3.14. A playing field is a rectangle 50 m long and 36 m wide with a semicircle 36 m across at each end. What is its area, in m²?
Working:
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15.Take π as 3.14. A round pond has a radius of 11 m, with a path 3 m wide all round it. What is the area of the path, in m²?
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16.Take π as 3.14. A round rug is 4 m across and costs $140 a square metre. How much is the rug?
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17.Take π as 3.14. A goat is tied with a 4 m rope at the corner where two walls meet at a right angle. At most, how big an area outside the walls can it graze, in m²?
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18.Take π as 3.14. A round pond has a radius of 10 m, with a path 2 m wide all round it. What is the area of the path, in m²?
Working:
Answer:

Show the answers and working

Areas of semicircles, rings and shapes made with them worksheet: Answers and working

1. 153.86
Find the whole circle's area first, 3.14 × 14 × 14, then take a quarter.
The whole circle: 3.14 × 14 × 14 = 615.44; a quarter: 615.44 ÷ 4 = 153.86.
2. 127.17
The picture gives the diameter, 18 cm. Find the radius, then the whole circle's area, then half of it.
The radius is 18 ÷ 2 = 9; the circle is 3.14 × 9 × 9 = 254.34, half of it 127.17.
3. 90.28
Split it in two: the rectangle 21 × 4, plus a semicircle of radius 2.
Rectangle 21 × 4 = 84; semicircle of radius 2: 3.14 × 2 × 2 ÷ 2 = 6.28; 84 + 6.28 = 90.28.
4. 160.14
A ring = big circle − small circle. Find the areas of the circles of radius 10 and 7 first.
Big circle 3.14 × 10 × 10 = 314, small 3.14 × 7 × 7 = 153.86; 314 − 153.86 = 160.14.
5. 86
Shaded part = square − quarter circle. Find the square's area first: 20 × 20.
Square 20 × 20 = 400; quarter circle 3.14 × 20 × 20 ÷ 4 = 314; 400 − 314 = 86.

6. C. 18.84
In the rectangle made from the slices, what part of the circumference is the length? And what is the width?
Its length is half the circumference: 3.14 × 6 = 18.84; its width is the radius 6, so the area is 3.14 × r × r.
7. A. 47.1
In the rectangle made from the slices, what part of the circumference is the length? And what is the width?
Its length is half the circumference: 3.14 × 15 = 47.1; its width is the radius 15, so the area is 3.14 × r × r.
8. A. 31.4
In the rectangle made from the slices, what part of the circumference is the length? And what is the width?
Its length is half the circumference: 3.14 × 10 = 31.4; its width is the radius 10, so the area is 3.14 × r × r.
9. True
6 cm is the diameter, but the area needs the radius. Find it, work out the semicircle and compare with 14.13.
Use the radius 3, not the diameter: 3.14 × 3 × 3 ÷ 2 = 14.13.
10. True
8 cm is the diameter, but the area needs the radius. Find it, work out the semicircle and compare with 25.12.
Use the radius 4, not the diameter: 3.14 × 4 × 4 ÷ 2 = 25.12.
11. False
14 cm is the diameter, but the area needs the radius. Find it, work out the semicircle and compare with 307.72.
Use the radius 7, not the diameter: 3.14 × 7 × 7 ÷ 2 = 76.93.
12. True
4 cm is the diameter, but the area needs the radius. Find it, work out the semicircle and compare with 6.28.
Use the radius 2, not the diameter: 3.14 × 2 × 2 ÷ 2 = 6.28.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 157 cm²
Find the whole pizza's area first, with radius 40 ÷ 2, then share it into 8.
Radius 20: 3.14 × 20 × 20 = 1256; 1256 ÷ 8 = 157.
14. 2817.36 m²
Split it up: the rectangle in the middle and the semicircles at the ends. The two semicircles make one circle.
Rectangle 50 × 36 = 1800; the semicircles make a circle of radius 18: 3.14 × 18 × 18 = 1017.36; 1800 + 1017.36 = 2817.36.
15. 235.5 m²
The path is a ring. Find the big circle's radius first: the pond's radius plus the path's width.
The big radius is 11 + 3 = 14; the path is a ring: 3.14 × (14 × 14 − 11 × 11) = 235.5.
16. 1758.4 dollars
Find the rug's area first: 4 m is the diameter, so halve it for the radius. Then times $140 a square metre.
Radius 2: area 3.14 × 2 × 2 = 12.56; 12.56 × 140 = 1758.4.
17. 12.56 m²
The walls block part of it: what fraction of a circle can the goat reach? The 4 m rope is the radius.
The walls leave it a quarter circle: 3.14 × 4 × 4 = 50.24, 50.24 ÷ 4 = 12.56.
18. 138.16 m²
The path is a ring. Find the big circle's radius first: the pond's radius plus the path's width.
The big radius is 10 + 2 = 12; the path is a ring: 3.14 × (12 × 12 − 10 × 10) = 138.16.

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