Perimeter, area and volume · Ages 11–12
Circumference and area of a circle worksheet
Covers: Circumference, Area of a circle, Circumference and area together, Perimeters of semicircles and shapes made with them, Areas of semicircles, rings and shapes made with them
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Circumference and area of a circle 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 circumference of this circle. (Take π as 3.14.) The answer is cm
Answer:
2.Take π as 227. What is the circumference of a circle 14 cm across, in cm?
Answer:
3.Find the area of this circle. (Take π as 3.14.) The answer is cm²
Answer:
4.Take π as 3.14. A circle's circumference is 6.28 cm. What is its area, in cm²?
Answer:
5.Radius = ? cm
Take π as 3.14
Answer:
6.Radius = ? cm
Take π as 3.14
Answer:
7.Take π as 3.14. A circle's circumference is 9.42 cm. How long is its diameter, in cm?
Answer:
8.The shape is a rectangle and a semicircle. Find its perimeter. (Take π as 3.14.) The answer is cm
Answer:
Part B: Choose, or true or false (2 marks each)
9.Which circle has the longest circumference?
- A. A circle 15 cm across
- B. A circle of radius 6 cm
- C. A circle of radius 7 cm
- D. A circle 13 cm across
Choose the right answer
Answer:
10.Take π as 3.14. What is the area of a circle of radius 11 cm, in cm²?
- A. 69.08
- B. 379.94
- C. 1519.76
- D. 34.54
Choose the right answer
Answer:
11.Take π as 3.14. A circle of radius 12 cm is cut into many equal slices and laid out as an almost-rectangle. About how long is the rectangle, in cm?
- A. 12
- B. 75.36
- C. 37.68
- D. 24
Choose the right answer
Answer:
12.A semicircle with a diameter of 4 cm has an area of 25.12 cm². (Take π as 3.14.)
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Take π as 3.14. Ka-yan's round table is 70 cm across. Lace goes once round its edge. At least how many centimetres of lace are needed?
Working:
Answer:
14.Take π as 3.14. A round pond is 34 m across. May runs 4 times round its edge. How many metres is that?
Working:
Answer:
15.Take π as 3.14. Ming's grandpa has a round flower bed of radius 2 m, and each square metre needs 50 g of plant food. How many grams does the whole bed need?
Working:
Answer:
16.A circular flower bed has a diameter of 16 m. What is its circumference, in metres? (Take π as 3.14.)
Answer as a decimal
Working:
Answer:
17.Take π as 3.14. A running track has two straights of 65 m and a semicircle 44 m across at each end. How many metres is one lap?
Working:
Answer:
18.Take π as 3.14. A round rug is 2 m across and costs $180 a square metre. How much is the rug?
Working:
Answer:
Show the answers and working
Circumference and area of a circle worksheet: Answers and working
Part A: Working out and filling in
1. 84.78
The 27 cm in the picture is the diameter. Circumference = 3.14 × diameter.
Circumference = 3.14 × diameter = 3.14 × 27 = 84.78.
2. 44 cm
Circumference = 227 × 14. 14 is a multiple of 7, so do 14 ÷ 7 first.
227 × 14 = 22 × 2 = 44: with a diameter in sevens, 227 is handy.
3. 314
The 10 cm in the picture is the radius. Area = 3.14 × r × r, so work out 10 × 10 first.
10 × 10 = 100; 3.14 × 100 = 314.
4. 3.14 cm²
The area needs the radius. Find the diameter from the circumference, 6.28 ÷ 3.14, then the radius.
Diameter = 6.28 ÷ 3.14 = 2, so the radius is 1; 3.14 × 1 × 1 = 3.14.
5. Radius = 8 cm
Diameter = circumference ÷ 3.14: 50.24 ÷ 3.14 = 16, and the radius is half of it, 16 ÷ 2 = 8, so 8
6. Radius = 4 cm
Diameter = circumference ÷ 3.14: 25.12 ÷ 3.14 = 8, and the radius is half of it, 8 ÷ 2 = 4, so 4
7. 3 cm
Circumference = 3.14 × diameter, so backwards, diameter = circumference ÷ 3.14.
Circumference = 3.14 × diameter, so backwards: 9.42 ÷ 3.14 = 3.
8. 67.98
Go round the outside: three straight edges and a semicircle's curve. The dashed line is inside, so it doesn't count.
Straight edges: 16 + 16 + 14 = 46 (the dashed line is inside, so not counted); the curve: 3.14 × 14 ÷ 2 = 21.98; 46 + 21.98 = 67.98.
Part B: Choose, or true or false
9. A. A circle 15 cm across
Some give the diameter and some the radius. Turn each into a diameter first, then compare.
Turn each into a diameter and compare: 15, 14, 13 and 12 cm; the longer the diameter, the longer the circumference, so the circle 15 cm across wins.
10. B. 379.94
Area is 3.14 × r × r, the radius twice. Work out 11 × 11 first.
3.14 × 11 × 11 = 379.94.
11. C. 37.68
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 × 12 = 37.68; its width is the radius 12, so the area is 3.14 × r × r.
12. False
4 cm is the diameter, but the area needs the radius. Find it, work out the semicircle and compare with 25.12.
Use the radius 2, not the diameter: 3.14 × 2 × 2 ÷ 2 = 6.28.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 219.8 cm
Once round is the circumference. The table is 70 cm across, and circumference = 3.14 × diameter.
Once round is the circumference: 3.14 × 70 = 219.8.
14. 427.04 m
Find one lap first, circumference = 3.14 × 34, then think about 4 laps.
One lap is 3.14 × 34 = 106.76 m; 4 laps are 106.76 × 4 = 427.04 m.
15. 628 g
Find the bed's area first, 3.14 × 2 × 2, then think about 50 g a square metre.
Area: 3.14 × 2 × 2 = 12.56 m²; 12.56 × 50 = 628 g.
16. A circular flower bed has a diameter of 16 m. What is its circumference, in metres? (Take π as 3.14.) (Answer: 50.24 m)
3.14 × 16 = 50.24
17. 268.16 m
The two end semicircles make one circle 44 m across; then add the two straights.
The two semicircles make one circle: 3.14 × 44 = 138.16; the straights 130; 130 + 138.16 = 268.16.
18. 565.2 dollars
Find the rug's area first: 2 m is the diameter, so halve it for the radius. Then times $180 a square metre.
Radius 1: area 3.14 × 1 × 1 = 3.14; 3.14 × 180 = 565.2.
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