Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 452 · 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 7 cm. What is its total surface area? (a) 49 sq cm (b) 196 sq cm (c) 294 sq cm (d) 343 sq cm
2. 2.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) 6 times (c) 27 times (d) 9 times
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) 2 times (c) 6 times (d) 4 times
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
5. 5.A cuboid is 11 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 119 sq cm (b) 476 sq cm (c) 220 sq cm (d) 238 sq cm
6. 6.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 576 cu cm
7. 7.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) 27 times (c) 6 times (d) 3 times
8. 8.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
10. 10.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
13. 13.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
14. 14.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
15. 15.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
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
17. 17.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
18. 18.A cuboid is 10 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 432 sq cm (b) 108 sq cm (c) 180 sq cm (d) 216 sq cm
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
20. 20.A cuboid is 7 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 222 sq cm (b) 111 sq cm (c) 444 sq cm (d) 189 sq cm
21. 21.If the side of a square 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
22. 22.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
23. 23.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
24. 24.A cuboid is 9 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 27 cu cm (b) 108 cu cm (c) 150 cu cm (d) 16 cu cm
25. 25.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 144 sq cm (d) 1728 sq cm
26. 26.A cuboid is 9 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 252 cu cm (b) 254 cu cm (c) 63 cu cm (d) 20 cu cm
27. 27.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 64 sq cm (b) 56 sq cm (c) 112 sq cm (d) 224 sq cm
28. 28.A cuboid is 10 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 120 cu cm (b) 164 cu cm (c) 17 cu cm (d) 40 cu cm
29. 29.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) 3 times (c) 27 times (d) 9 times
30. 30.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
31. 31.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 10 cu cm (b) 62 cu cm (c) 6 cu cm (d) 30 cu cm
32. 32.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
33. 33.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
34. 34.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
35. 35.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
36. 36.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
37. 37.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 217 sq cm (d) 216 sq cm
38. 38.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
39. 39.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
40. 40.A cuboid is 12 cm long, 11 cm wide and 7 cm high. What is its total surface area? (a) 924 sq cm (b) 293 sq cm (c) 1172 sq cm (d) 586 sq cm

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