Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 625 · 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) 217 cu cm (b) 18 cu cm (c) 216 cu cm (d) 144 cu cm
2. 2.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) 25 times (d) 125 times
3. 3.A cuboid is 8 cm long, 7 cm wide and 7 cm high. What is its volume? (a) 392 cu cm (b) 322 cu cm (c) 56 cu cm (d) 22 cu cm
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
5. 5.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 36 sq cm (d) 27 sq cm
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
7. 7.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 51 sq cm (b) 102 sq cm (c) 54 sq cm (d) 204 sq cm
8. 8.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) 4 times (d) 2 times
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
10. 10.A cuboid is 11 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 132 sq cm (b) 400 sq cm (c) 100 sq cm (d) 200 sq cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
12. 12.A cuboid is 7 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 210 cu cm (b) 18 cu cm (c) 214 cu cm (d) 35 cu cm
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
14. 14.A cuboid is 9 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 300 sq cm (b) 150 sq cm (c) 108 sq cm (d) 75 sq cm
15. 15.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
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
17. 17.A cuboid is 8 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 240 sq cm (b) 134 sq cm (c) 536 sq cm (d) 268 sq cm
18. 18.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
19. 19.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
20. 20.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
21. 21.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
22. 22.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
23. 23.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 384 cu cm (d) 24 cu cm
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
25. 25.A cuboid is 9 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 51 sq cm (b) 204 sq cm (c) 54 sq cm (d) 102 sq cm
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
27. 27.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
30. 30.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) 2 times (c) 4 times (d) 6 times
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
32. 32.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) 3 times (c) 6 times (d) 27 times
33. 33.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 97 sq cm (d) 16 sq cm
34. 34.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 96 cu cm (c) 12 cu cm (d) 65 cu cm
35. 35.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) 27 times (c) 9 times (d) 3 times
36. 36.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
37. 37.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) 5 times (d) 25 times
38. 38.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 12 sq cm (b) 32 sq cm (c) 16 sq cm (d) 64 sq cm
39. 39.A cuboid is 11 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 396 cu cm (b) 23 cu cm (c) 66 cu cm (d) 336 cu cm
40. 40.A cuboid is 10 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 120 cu cm (b) 30 cu cm (c) 17 cu cm (d) 164 cu cm

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