Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 322 · 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.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
2. 2.A cuboid is 8 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 120 sq cm (b) 316 sq cm (c) 158 sq cm (d) 79 sq cm
3. 3.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
5. 5.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 216 sq cm (d) 217 sq cm
6. 6.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 10 cu cm (b) 12 cu cm (c) 50 cu cm (d) 90 cu cm
7. 7.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
8. 8.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
10. 10.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) 5 times (c) 125 times (d) 10 times
11. 11.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 256 cu cm (d) 24 cu cm
12. 12.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
13. 13.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
14. 14.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
15. 15.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
16. 16.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 52 cu cm (b) 9 cu cm (c) 24 cu cm (d) 8 cu cm
17. 17.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
18. 18.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
19. 19.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
20. 20.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 576 cu cm (d) 36 cu cm
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
23. 23.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 12 cu cm (b) 136 cu cm (c) 15 cu cm (d) 96 cu cm
24. 24.A cuboid is 12 cm long, 9 cm wide and 4 cm high. What is its total surface area? (a) 384 sq cm (b) 432 sq cm (c) 768 sq cm (d) 192 sq cm
25. 25.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 272 sq cm (b) 68 sq cm (c) 136 sq cm (d) 80 sq cm
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
28. 28.A cuboid is 12 cm long, 7 cm wide and 7 cm high. What is its volume? (a) 84 cu cm (b) 434 cu cm (c) 588 cu cm (d) 26 cu cm
29. 29.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
30. 30.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
31. 31.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
32. 32.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
33. 33.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 110 sq cm (b) 200 sq cm (c) 220 sq cm (d) 440 sq cm
34. 34.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) 3 times (c) 9 times (d) 27 times
35. 35.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 64 sq cm (d) 16 sq cm
36. 36.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 27 sq cm (d) 36 sq cm
37. 37.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
38. 38.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 2 times (d) 8 times
40. 40.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 36 cu cm (b) 12 cu cm (c) 11 cu cm (d) 72 cu cm

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