Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 778 · 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 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 150 sq cm (d) 125 sq cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
3. 3.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 2 times (d) 4 times
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
7. 7.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
8. 8.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 343 cu cm (d) 21 cu cm
9. 9.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
11. 11.A cuboid is 6 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 64 sq cm (c) 96 sq cm (d) 256 sq cm
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
16. 16.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 400 sq cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 6 cu cm (b) 7 cu cm (c) 32 cu cm (d) 12 cu cm
18. 18.A cuboid is 6 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 15 cu cm (d) 108 cu cm
19. 19.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
20. 20.If the radius of a circle 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
21. 21.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 256 sq cm (d) 64 sq cm
22. 22.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
23. 23.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
24. 24.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
25. 25.A cuboid is 11 cm long, 7 cm wide and 3 cm high. What is its total surface area? (a) 524 sq cm (b) 262 sq cm (c) 131 sq cm (d) 231 sq cm
26. 26.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 9 sq cm (d) 54 sq cm
27. 27.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 30 cu cm (b) 280 cu cm (c) 21 cu cm (d) 300 cu cm
28. 28.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 486 cu cm (d) 729 cu cm
29. 29.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
30. 30.A cuboid is 11 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 334 sq cm (b) 668 sq cm (c) 167 sq cm (d) 385 sq cm
31. 31.A cuboid is 11 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 15 cu cm (b) 44 cu cm (c) 22 cu cm (d) 96 cu cm
32. 32.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
33. 33.A cuboid is 11 cm long, 9 cm wide and 2 cm high. What is its total surface area? (a) 198 sq cm (b) 278 sq cm (c) 139 sq cm (d) 556 sq cm
34. 34.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
35. 35.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 486 sq cm (d) 324 sq cm
36. 36.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 46 sq cm (b) 184 sq cm (c) 92 sq cm (d) 48 sq cm
37. 37.A cuboid is 12 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 108 sq cm (b) 216 sq cm (c) 432 sq cm (d) 144 sq cm
38. 38.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
39. 39.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 30 cu cm
40. 40.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) 5 times (c) 125 times (d) 25 times

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