Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 277 · 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 6 cm. What is its volume? (a) 144 cu cm (b) 216 cu cm (c) 217 cu cm (d) 18 cu cm
2. 2.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
3. 3.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
4. 4.A cuboid is 7 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 172 sq cm (b) 344 sq cm (c) 86 sq cm (d) 112 sq cm
5. 5.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
6. 6.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
7. 7.What is the circumference of a circle of diameter 70 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 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
9. 9.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
10. 10.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
11. 11.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) 16 times (c) 64 times (d) 4 times
12. 12.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
13. 13.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 8 times (c) 4 times (d) 2 times
14. 14.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
16. 16.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 484 sq cm (c) 121 sq cm (d) 1331 sq cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
19. 19.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 384 sq cm (d) 64 sq cm
20. 20.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
21. 21.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
22. 22.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
23. 23.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 75 sq cm (c) 108 sq cm (d) 300 sq cm
24. 24.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 168 sq cm (b) 404 sq cm (c) 101 sq cm (d) 202 sq cm
25. 25.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 136 cu cm (b) 14 cu cm (c) 84 cu cm (d) 15 cu cm
26. 26.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 216 sq cm (c) 36 sq cm (d) 217 sq cm
27. 27.A cuboid is 7 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 118 sq cm (b) 236 sq cm (c) 59 sq cm (d) 70 sq cm
28. 28.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) 3 times (c) 27 times (d) 9 times
29. 29.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) 27 times (c) 6 times (d) 9 times
30. 30.A cuboid is 8 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 96 cu cm (b) 16 cu cm (c) 152 cu cm (d) 48 cu cm
31. 31.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
32. 32.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
33. 33.A cuboid is 8 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 560 cu cm (b) 412 cu cm (c) 25 cu cm (d) 56 cu cm
34. 34.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
36. 36.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
37. 37.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 324 sq cm (c) 486 sq cm (d) 729 sq cm
38. 38.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 61 sq cm (b) 244 sq cm (c) 84 sq cm (d) 122 sq cm
39. 39.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 380 sq cm (b) 190 sq cm (c) 126 sq cm (d) 95 sq cm
40. 40.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm

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