Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 346 · 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 circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
2. 2.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
3. 3.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 486 cu cm (d) 324 cu cm
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 6 times (d) 8 times
6. 6.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) 64 times (c) 4 times (d) 16 times
7. 7.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
10. 10.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
11. 11.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
12. 12.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 384 cu cm (d) 256 cu cm
13. 13.A cuboid is 9 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 101 sq cm (b) 404 sq cm (c) 180 sq cm (d) 202 sq cm
14. 14.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
15. 15.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 96 sq cm (d) 16 sq cm
16. 16.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) 8 times (c) 64 times (d) 4 times
17. 17.A cuboid is 5 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 260 sq cm (b) 65 sq cm (c) 100 sq cm (d) 130 sq cm
18. 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 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.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
21. 21.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
22. 22.A cuboid is 7 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 28 cu cm (b) 56 cu cm (c) 100 cu cm (d) 13 cu cm
23. 23.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
25. 25.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 9 cu cm (b) 52 cu cm (c) 8 cu cm (d) 24 cu cm
26. 26.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 65 sq cm (c) 64 sq cm (d) 32 sq cm
27. 27.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 196 sq cm (c) 343 sq cm (d) 294 sq cm
28. 28.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
29. 29.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
30. 30.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) 9 times (d) 3 times
31. 31.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 576 cu cm (c) 1728 cu cm (d) 864 cu cm
32. 32.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
33. 33.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
34. 34.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
35. 35.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 21 cu cm (d) 196 cu cm
36. 36.A cuboid is 11 cm long, 9 cm wide and 9 cm high. What is its volume? (a) 29 cu cm (b) 891 cu cm (c) 99 cu cm (d) 558 cu cm
37. 37.A cuboid is 8 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 112 cu cm (b) 16 cu cm (c) 17 cu cm (d) 172 cu cm
38. 38.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 24 sq cm (d) 4 sq cm
39. 39.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
40. 40.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm

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