Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 960 · 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.A cuboid is 11 cm long, 9 cm wide and 10 cm high. What is its volume? (a) 99 cu cm (b) 30 cu cm (c) 990 cu cm (d) 598 cu cm
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
5. 5.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
6. 6.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
8. 8.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
9. 9.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 8 times (c) 6 times (d) 4 times
10. 10.A cuboid is 9 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 102 cu cm (b) 14 cu cm (c) 27 cu cm (d) 54 cu cm
11. 11.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
12. 12.A cuboid is 12 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 372 sq cm (b) 744 sq cm (c) 186 sq cm (d) 360 sq cm
13. 13.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
14. 14.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
15. 15.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
16. 16.A cuboid is 12 cm long, 8 cm wide and 8 cm high. What is its volume? (a) 512 cu cm (b) 28 cu cm (c) 768 cu cm (d) 96 cu cm
17. 17.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
18. 18.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
19. 19.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) 16 times (c) 8 times (d) 64 times
20. 20.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 16 cu cm (b) 40 cu cm (c) 8 cu cm (d) 17 cu cm
21. 21.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
22. 22.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 84 sq cm (b) 42 sq cm (c) 18 sq cm (d) 21 sq cm
23. 23.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
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
25. 25.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
26. 26.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 400 sq cm (c) 600 sq cm (d) 100 sq cm
27. 27.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 97 sq cm (d) 96 sq cm
28. 28.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
29. 29.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 864 cu cm (d) 1728 cu cm
30. 30.A cuboid is 6 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 12 cu cm (b) 88 cu cm (c) 49 cu cm (d) 48 cu cm
31. 31.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 24 cu cm (d) 256 cu cm
32. 32.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
33. 33.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
34. 34.A cuboid is 10 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 166 sq cm (b) 360 sq cm (c) 664 sq cm (d) 332 sq cm
35. 35.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 172 cu cm (b) 56 cu cm (c) 17 cu cm (d) 112 cu cm
36. 36.A cuboid is 10 cm long, 7 cm wide and 9 cm high. What is its volume? (a) 70 cu cm (b) 26 cu cm (c) 446 cu cm (d) 630 cu cm
37. 37.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 36 sq cm (b) 73 sq cm (c) 72 sq cm (d) 144 sq cm
38. 38.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
39. 39.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 72 cu cm (b) 11 cu cm (c) 36 cu cm (d) 6 cu cm
40. 40.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times

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