Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 296 · 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 10 cm. What is its volume? (a) 400 cu cm (b) 30 cu cm (c) 600 cu cm (d) 1000 cu cm
2. 2.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
3. 3.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) 10 times (d) 5 times
4. 4.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
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
6. 6.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
9. 9.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 100 sq cm (c) 25 sq cm (d) 125 sq cm
10. 10.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
11. 11.A cuboid is 7 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 105 sq cm (b) 420 sq cm (c) 210 sq cm (d) 196 sq cm
12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
13. 13.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 24 sq cm (c) 16 sq cm (d) 4 sq cm
14. 14.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
15. 15.A cuboid is 8 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 344 sq cm (b) 172 sq cm (c) 86 sq cm (d) 112 sq cm
16. 16.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
17. 17.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 81 sq cm (d) 729 sq cm
18. 18.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
19. 19.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
20. 20.A cuboid is 12 cm long, 10 cm wide and 2 cm high. What is its total surface area? (a) 656 sq cm (b) 240 sq cm (c) 328 sq cm (d) 164 sq cm
21. 21.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
22. 22.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
23. 23.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) 5 times (c) 2 times (d) 8 times
24. 24.A cuboid is 8 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 152 cu cm (b) 16 cu cm (c) 48 cu cm (d) 96 cu cm
25. 25.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) 8 cu cm (d) 124 cu cm
26. 26.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
27. 27.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 8 cu cm (b) 64 cu cm (c) 14 cu cm (d) 112 cu cm
28. 28.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) 27 times (c) 9 times (d) 3 times
29. 29.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 576 sq cm (c) 144 sq cm (d) 864 sq cm
30. 30.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 152 sq cm (b) 40 sq cm (c) 38 sq cm (d) 76 sq cm
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
32. 32.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
33. 33.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 9 cu cm (c) 36 cu cm (d) 54 cu cm
34. 34.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 16 sq cm (c) 64 sq cm (d) 97 sq cm
35. 35.A cuboid is 10 cm long, 9 cm wide and 2 cm high. What is its total surface area? (a) 180 sq cm (b) 512 sq cm (c) 256 sq cm (d) 128 sq cm
36. 36.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 144 sq cm (d) 216 sq cm
37. 37.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
38. 38.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
39. 39.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
40. 40.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm

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