Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 774 · 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, 6 cm wide and 8 cm high. What is its volume? (a) 25 cu cm (b) 66 cu cm (c) 528 cu cm (d) 404 cu cm
2. 2.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
5. 5.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 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) 4 times (c) 5 times (d) 2 times
7. 7.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
8. 8.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) 9 times (c) 6 times (d) 3 times
9. 9.A cuboid is 7 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 68 sq cm (b) 84 sq cm (c) 136 sq cm (d) 272 sq cm
10. 10.A cuboid is 12 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 16 cu cm (b) 24 cu cm (c) 104 cu cm (d) 48 cu cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
12. 12.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
13. 13.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
15. 15.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
16. 16.A cuboid is 12 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 122 sq cm (b) 488 sq cm (c) 168 sq cm (d) 244 sq cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
18. 18.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 144 sq cm
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
20. 20.A cuboid is 7 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 292 sq cm (b) 584 sq cm (c) 336 sq cm (d) 146 sq cm
21. 21.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
22. 22.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
23. 23.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 196 sq cm (c) 49 sq cm (d) 343 sq cm
24. 24.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
25. 25.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
26. 26.A cuboid is 11 cm long, 9 cm wide and 7 cm high. What is its volume? (a) 478 cu cm (b) 693 cu cm (c) 99 cu cm (d) 27 cu cm
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
28. 28.A cuboid is 7 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 84 sq cm (b) 61 sq cm (c) 122 sq cm (d) 244 sq cm
29. 29.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) 10 times (c) 25 times (d) 5 times
30. 30.A cuboid is 8 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 268 cu cm (b) 21 cu cm (c) 240 cu cm (d) 24 cu cm
31. 31.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
32. 32.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
33. 33.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) 4 times (c) 8 times (d) 2 times
34. 34.A cuboid is 9 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 216 sq cm (b) 456 sq cm (c) 228 sq cm (d) 114 sq cm
35. 35.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) 16 times (c) 4 times (d) 64 times
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
37. 37.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 256 cu cm (d) 512 cu cm
38. 38.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
39. 39.A cuboid is 8 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 146 sq cm (b) 292 sq cm (c) 336 sq cm (d) 584 sq cm
40. 40.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 144 sq cm (d) 217 sq cm

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