Perimeter, area and volume · Ages 11–12
Perimeters of semicircles and shapes made with them worksheet
Part of: Circumference and area of a circle
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Perimeters of semicircles and shapes made with them worksheet
Perimeter, area and volume · Ages 11–12
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Find the perimeter of this semicircle. (Take π as 3.14.) The answer is cm
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2.Take π as 3.14. A circle's circumference is 75.36 cm. How long is its diameter, in cm?
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3.Take π as 3.14. A circle's circumference is 37.68 cm. How long is its diameter, in cm?
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4.Take π as 3.14. A circle's circumference is 94.2 cm. How long is its diameter, in cm?
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5.Take π as 3.14. A circle's circumference is 25.12 cm. How long is its radius, in cm?
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6.Find the perimeter of this quarter circle. (Take π as 3.14.) The answer is cm
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7.The curved part of this semicircle is cm long. (Take π as 3.14.)
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8.Take π as 3.14. A circle's circumference is 12.56 cm. How long is its radius, in cm?
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9.The shape is a rectangle and a semicircle. Find its perimeter. (Take π as 3.14.) The answer is cm
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Part B: Choose, or true or false (2 marks each)
10.A semicircle with a diameter of 20 cm has a perimeter of 51.4 cm. (Take π as 3.14.)
True or false?
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11.A semicircle with a diameter of 12 cm has a perimeter of 18.84 cm. (Take π as 3.14.)
True or false?
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12.A semicircle with a diameter of 4 cm has a perimeter of 6.28 cm. (Take π as 3.14.)
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Take π as 3.14. Chi-keung's bike wheel is 45 cm across. The wheel turns 130 times. How many metres does the bike go?
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14.Take π as 3.14. In a corner of two walls is a quarter-circle flower bed of radius 7 m. The straight edges are against the walls, so only the curved edge needs a fence. How long is the fence, in m?
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15.Take π as 3.14. A running track has two straights of 80 m and a semicircle 58 m across at each end. How many metres is one lap?
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16.Take π as 3.14. A round flower bed has a circumference of 131.88 m. What is its radius, in metres?
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17.Take π as 3.14. A semicircular window is 100 cm across. Aluminium strip goes all round it, the straight edge too. How many centimetres of strip are needed?
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18.Take π as 3.14. A round flower bed has a circumference of 87.92 m. What is its radius, in metres?
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Show the answers and working
Perimeters of semicircles and shapes made with them worksheet: Answers and working
Part A: Working out and filling in
1. 38.55
A semicircle's perimeter is the curve plus the diameter. Find the curve first: half the circumference.
The curve: 3.14 × 15 ÷ 2 = 23.55; add the diameter: 23.55 + 15 = 38.55.
2. 24 cm
Circumference = 3.14 × diameter, so backwards, diameter = circumference ÷ 3.14.
Circumference = 3.14 × diameter, so backwards: 75.36 ÷ 3.14 = 24.
3. 12 cm
Circumference = 3.14 × diameter, so backwards, diameter = circumference ÷ 3.14.
Circumference = 3.14 × diameter, so backwards: 37.68 ÷ 3.14 = 12.
4. 30 cm
Circumference = 3.14 × diameter, so backwards, diameter = circumference ÷ 3.14.
Circumference = 3.14 × diameter, so backwards: 94.2 ÷ 3.14 = 30.
5. 4 cm
Find the diameter from the circumference first, 25.12 ÷ 3.14, then think how the radius relates to it.
Diameter = 25.12 ÷ 3.14 = 8; the radius is half of it: 8 ÷ 2 = 4.
6. 28.56
A quarter circle's perimeter is a curve and two radii. Find the curve first: a quarter of the circumference, diameter 16.
The curve is a quarter of the circumference: 3.14 × 16 ÷ 4 = 12.56; add two radii: 12.56 + 16 = 28.56.
7. 15.7
Only the curve counts: it is half the circumference of a circle 10 cm across.
Only the curve: half the circumference, 3.14 × 10 ÷ 2 = 15.7.
8. 2 cm
Find the diameter from the circumference first, 12.56 ÷ 3.14, then think how the radius relates to it.
Diameter = 12.56 ÷ 3.14 = 4; the radius is half of it: 4 ÷ 2 = 2.
9. 94.26
Go round the outside: three straight edges and a semicircle's curve. The dashed line is inside, so it doesn't count.
Straight edges: 24 + 24 + 18 = 66 (the dashed line is inside, so not counted); the curve: 3.14 × 18 ÷ 2 = 28.26; 66 + 28.26 = 94.26.
Part B: Choose, or true or false
10. True
A semicircle's perimeter includes the curve and the straight diameter. Check whether 51.4 counts both.
The perimeter is the curve and the diameter: 3.14 × 20 ÷ 2 + 20 = 51.4.
11. False
A semicircle's perimeter includes the curve and the straight diameter. Check whether 18.84 counts both.
The perimeter is the curve and the diameter: 3.14 × 12 ÷ 2 + 12 = 30.84.
12. False
A semicircle's perimeter includes the curve and the straight diameter. Check whether 6.28 counts both.
The perimeter is the curve and the diameter: 3.14 × 4 ÷ 2 + 4 = 10.28.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 183.69 m
Each turn moves the bike one circumference. Work out 3.14 × 45 first, and change to metres at the end.
One turn goes one circumference: 3.14 × 45 = 141.3 cm; 130 turns are 141.3 × 130 cm = 183.69 m.
14. 10.99 m
Only the curve needs a fence: a quarter of the circumference of a circle of radius 7 m. Find the diameter first.
Only the curve: a quarter of the circumference, 3.14 × 14 ÷ 4 = 10.99.
15. 342.12 m
The two end semicircles make one circle 58 m across; then add the two straights.
The two semicircles make one circle: 3.14 × 58 = 182.12; the straights 160; 160 + 182.12 = 342.12.
16. 21 m
Find the diameter from the circumference first, 131.88 ÷ 3.14, then think what part of it the radius is.
Diameter = 131.88 ÷ 3.14 = 42; radius = 42 ÷ 2 = 21.
17. 257 cm
The strip goes round the curve and the straight edge. Find the curve first: half the circumference.
The curve 3.14 × 100 ÷ 2 = 157; plus the straight edge: 157 + 100 = 257.
18. 14 m
Find the diameter from the circumference first, 87.92 ÷ 3.14, then think what part of it the radius is.
Diameter = 87.92 ÷ 3.14 = 28; radius = 28 ÷ 2 = 14.
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