Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 400 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
5. 5.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
6. 6.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
8. 8.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 6 times (d) 2 times
9. 9.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 125 sq cm (c) 100 sq cm (d) 25 sq cm
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
11. 11.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
12. 12.A cuboid is 8 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 97 cu cm (b) 96 cu cm (c) 16 cu cm (d) 152 cu cm
13. 13.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
14. 14.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 217 sq cm (c) 36 sq cm (d) 144 sq cm
15. 15.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 400 cu cm (c) 600 cu cm (d) 30 cu cm
16. 16.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
17. 17.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
19. 19.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
20. 20.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
22. 22.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
23. 23.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
24. 24.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 864 sq cm
25. 25.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
26. 26.A cuboid is 8 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 32 cu cm (b) 15 cu cm (c) 136 cu cm (d) 96 cu cm
27. 27.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
28. 28.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 18 cu cm (b) 202 cu cm (c) 21 cu cm (d) 168 cu cm
29. 29.A cuboid is 7 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 224 cu cm (b) 232 cu cm (c) 28 cu cm (d) 19 cu cm
30. 30.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
31. 31.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 81 sq cm (c) 324 sq cm (d) 729 sq cm
32. 32.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 84 cu cm (b) 15 cu cm (c) 14 cu cm (d) 136 cu cm
33. 33.A cuboid is 11 cm long, 10 cm wide and 5 cm high. What is its volume? (a) 550 cu cm (b) 110 cu cm (c) 26 cu cm (d) 430 cu cm
34. 34.A cuboid is 9 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 202 cu cm (b) 45 cu cm (c) 18 cu cm (d) 180 cu cm
35. 35.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 160 sq cm (b) 48 sq cm (c) 40 sq cm (d) 80 sq cm
36. 36.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
37. 37.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
38. 38.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
39. 39.A cuboid is 6 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 24 sq cm (b) 28 sq cm (c) 112 sq cm (d) 56 sq cm
40. 40.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm

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