Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 157 · 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 cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 324 cu cm (d) 486 cu cm
2. 2.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
3. 3.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
5. 5.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
6. 6.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 512 sq cm (d) 256 sq cm
7. 7.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
9. 9.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 726 cu cm (c) 33 cu cm (d) 484 cu cm
10. 10.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
11. 11.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq 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) 8 times (b) 2 times (c) 4 times (d) 5 times
14. 14.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 576 sq cm (d) 1728 sq cm
15. 15.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
16. 16.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
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
19. 19.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 102 sq cm (b) 54 sq cm (c) 51 sq cm (d) 204 sq cm
20. 20.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 400 cu cm (d) 600 cu cm
21. 21.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
22. 22.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 8 times (d) 2 times
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) 16 times (c) 4 times (d) 64 times
24. 24.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
25. 25.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
26. 26.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 125 cu cm (d) 15 cu cm
27. 27.A cuboid is 9 cm long, 8 cm wide and 10 cm high. What is its volume? (a) 720 cu cm (b) 484 cu cm (c) 27 cu cm (d) 72 cu cm
28. 28.A cuboid is 12 cm long, 11 cm wide and 4 cm high. What is its volume? (a) 448 cu cm (b) 528 cu cm (c) 132 cu cm (d) 27 cu cm
29. 29.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) 5 times (d) 25 times
30. 30.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 196 cu cm (c) 21 cu cm (d) 294 cu cm
31. 31.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
32. 32.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 512 cu cm (d) 24 cu cm
33. 33.A cuboid is 9 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 20 cu cm (b) 254 cu cm (c) 252 cu cm (d) 36 cu cm
34. 34.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 96 sq cm (b) 76 sq cm (c) 304 sq cm (d) 152 sq cm
35. 35.A cuboid is 7 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 136 sq cm (b) 272 sq cm (c) 68 sq cm (d) 84 sq cm
36. 36.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 65 cu cm (d) 64 cu cm
37. 37.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
38. 38.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
39. 39.A cuboid is 6 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 288 sq cm (b) 108 sq cm (c) 144 sq cm (d) 72 sq cm
40. 40.A cuboid is 6 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 20 cu cm (b) 258 cu cm (c) 30 cu cm (d) 270 cu cm

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