Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 260 · 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 8 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 17 cu cm (b) 144 cu cm (c) 24 cu cm (d) 180 cu cm
2. 2.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 65 cu cm (c) 12 cu cm (d) 96 cu cm
3. 3.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 31 sq cm (b) 124 sq cm (c) 30 sq cm (d) 62 sq cm
4. 4.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 25 sq cm (d) 150 sq cm
5. 5.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 15 cu cm (b) 14 cu cm (c) 126 cu cm (d) 90 cu cm
6. 6.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 294 cu cm (d) 21 cu cm
7. 7.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
8. 8.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
9. 9.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
11. 11.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
12. 12.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) 6 times (c) 8 times (d) 4 times
13. 13.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 180 sq cm (b) 108 sq cm (c) 432 sq cm (d) 216 sq cm
14. 14.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
15. 15.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) 25 times (c) 10 times (d) 125 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) 9 times (b) 6 times (c) 3 times (d) 27 times
17. 17.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
18. 18.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
19. 19.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
20. 20.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
21. 21.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
23. 23.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 576 sq cm (c) 864 sq cm (d) 1728 sq cm
24. 24.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 14 cu cm (b) 18 cu cm (c) 126 cu cm (d) 190 cu cm
25. 25.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
26. 26.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 30 sq cm (b) 31 sq cm (c) 124 sq cm (d) 62 sq cm
27. 27.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 1728 cu cm (c) 864 cu cm (d) 576 cu cm
28. 28.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
29. 29.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) 8 times (d) 16 times
30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
31. 31.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
32. 32.A cuboid is 5 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 20 cu cm (b) 14 cu cm (c) 100 cu cm (d) 130 cu cm
33. 33.A cuboid is 8 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 72 sq cm (b) 114 sq cm (c) 228 sq cm (d) 57 sq cm
34. 34.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 15 cu cm (b) 72 cu cm (c) 124 cu cm (d) 8 cu cm
35. 35.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 486 sq cm (d) 729 sq cm
36. 36.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
37. 37.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 48 cu cm (b) 12 cu cm (c) 80 cu cm (d) 11 cu cm
38. 38.A cuboid is 9 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 27 cu cm (b) 15 cu cm (c) 126 cu cm (d) 81 cu cm
39. 39.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 30 cu cm
40. 40.A cuboid is 8 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 236 cu cm (b) 40 cu cm (c) 19 cu cm (d) 240 cu cm

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