Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 31 · 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 radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
2. 2.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
3. 3.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 84 sq cm (b) 122 sq cm (c) 61 sq cm (d) 244 sq cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
7. 7.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
9. 9.A cuboid is 11 cm long, 8 cm wide and 4 cm high. What is its total surface area? (a) 328 sq cm (b) 656 sq cm (c) 164 sq cm (d) 352 sq cm
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
11. 11.A cuboid is 12 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 256 sq cm (b) 512 sq cm (c) 240 sq cm (d) 128 sq cm
12. 12.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
13. 13.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
14. 14.A cuboid is 5 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 83 sq cm (b) 166 sq cm (c) 332 sq cm (d) 140 sq cm
15. 15.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
16. 16.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 294 cu cm (d) 343 cu 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) 693 sq cm (d) 5544 sq cm
18. 18.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
19. 19.A cuboid is 11 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 495 sq cm (b) 796 sq cm (c) 398 sq cm (d) 199 sq cm
20. 20.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
22. 22.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 576 sq cm (d) 144 sq 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) 64 times (b) 16 times (c) 4 times (d) 8 times
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
25. 25.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
26. 26.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
27. 27.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 24 cu cm (b) 228 cu cm (c) 216 cu cm (d) 19 cu cm
28. 28.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 24 cu cm (d) 8 cu cm
29. 29.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
30. 30.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 17 cu cm (b) 18 cu cm (c) 180 cu cm (d) 144 cu cm
31. 31.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 217 sq cm (d) 144 sq cm
32. 32.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
33. 33.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
34. 34.A cuboid is 12 cm long, 9 cm wide and 10 cm high. What is its total surface area? (a) 636 sq cm (b) 318 sq cm (c) 1272 sq cm (d) 1080 sq cm
35. 35.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
36. 36.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 384 cu cm (d) 512 cu cm
37. 37.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
38. 38.A cuboid is 12 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 432 cu cm (b) 384 cu cm (c) 108 cu cm (d) 25 cu cm
39. 39.If the side of a square 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
40. 40.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm

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