Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 897 · 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 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
2. 2.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
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
4. 4.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
5. 5.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 216 sq cm (b) 492 sq cm (c) 123 sq cm (d) 246 sq cm
6. 6.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
7. 7.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 600 sq cm (c) 400 sq cm (d) 100 sq cm
8. 8.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
9. 9.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
10. 10.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 8 cu cm (d) 16 cu cm
11. 11.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
12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
13. 13.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
14. 14.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 343 cu cm (d) 294 cu cm
15. 15.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
16. 16.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
17. 17.A cuboid is 11 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 356 sq cm (b) 89 sq cm (c) 132 sq cm (d) 178 sq cm
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
19. 19.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
20. 20.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
21. 21.A cuboid is 9 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 512 sq cm (b) 128 sq cm (c) 180 sq cm (d) 256 sq cm
22. 22.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
23. 23.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 16 sq cm (d) 24 sq cm
24. 24.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
25. 25.A cuboid is 11 cm long, 8 cm wide and 6 cm high. What is its volume? (a) 88 cu cm (b) 528 cu cm (c) 25 cu cm (d) 404 cu cm
26. 26.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 9 sq cm (d) 54 sq cm
27. 27.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
28. 28.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
29. 29.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
30. 30.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 46 sq cm (b) 184 sq cm (c) 48 sq cm (d) 92 sq cm
31. 31.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) 4 times (d) 5 times
32. 32.A cuboid is 11 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 796 sq cm (b) 495 sq cm (c) 199 sq cm (d) 398 sq cm
33. 33.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 72 cu cm (b) 6 cu cm (c) 36 cu cm (d) 11 cu cm
34. 34.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 122 cu cm (b) 14 cu cm (c) 84 cu cm (d) 12 cu cm
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
37. 37.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 343 sq cm (d) 294 sq cm
38. 38.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) 2 times (c) 4 times (d) 8 times
39. 39.A cuboid is 12 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 23 cu cm (b) 320 cu cm (c) 48 cu cm (d) 336 cu cm
40. 40.A cuboid is 11 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 55 cu cm (b) 24 cu cm (c) 440 cu cm (d) 366 cu cm

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