Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 849 · 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 radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
2. 2.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 180 sq cm (b) 216 sq cm (c) 108 sq cm (d) 432 sq cm
3. 3.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
5. 5.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
6. 6.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 256 cu cm (c) 512 cu cm (d) 384 cu cm
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
8. 8.A cuboid is 10 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 20 cu cm (b) 160 cu cm (c) 100 cu cm (d) 17 cu 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 area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
11. 11.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) 5 times (c) 2 times (d) 4 times
12. 12.A cuboid is 7 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 28 cu cm (b) 280 cu cm (c) 21 cu cm (d) 276 cu cm
13. 13.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) 6 times (c) 9 times (d) 27 times
14. 14.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
16. 16.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 63 sq cm (b) 90 sq cm (c) 252 sq cm (d) 126 sq cm
17. 17.What is the area of a circle of radius 14 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 8 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 13 cu cm (b) 24 cu cm (c) 92 cu cm (d) 48 cu cm
19. 19.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 4 sq cm (d) 8 sq cm
20. 20.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
21. 21.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 56 cu cm (b) 8 cu cm (c) 100 cu cm (d) 13 cu cm
22. 22.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) 10 times (c) 25 times (d) 5 times
23. 23.If the side of a square 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
24. 24.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
25. 25.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) 4 times (c) 16 times (d) 8 times
26. 26.A cuboid is 12 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 108 sq cm (b) 216 sq cm (c) 432 sq cm (d) 144 sq cm
27. 27.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 84 cu cm (b) 136 cu cm (c) 14 cu cm (d) 15 cu cm
28. 28.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
29. 29.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
30. 30.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
31. 31.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 560 sq cm (b) 300 sq cm (c) 280 sq cm (d) 140 sq cm
32. 32.A cuboid is 10 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 30 cu cm (b) 150 cu cm (c) 190 cu cm (d) 18 cu cm
33. 33.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 27 cu cm (d) 54 cu cm
34. 34.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
35. 35.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
36. 36.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
37. 37.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
38. 38.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 64 sq cm (c) 256 sq cm (d) 384 sq cm
39. 39.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 90 cu cm (b) 14 cu cm (c) 15 cu cm (d) 126 cu cm
40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm

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