Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 262 · 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 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 16 sq cm (d) 96 sq cm
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 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) 10 times (b) 25 times (c) 125 times (d) 5 times
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq 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) 4 times (b) 16 times (c) 8 times (d) 64 times
10. 10.A cuboid is 12 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 720 cu cm (b) 72 cu cm (c) 504 cu cm (d) 28 cu cm
11. 11.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
12. 12.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
13. 13.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 39 sq cm (b) 78 sq cm (c) 156 sq cm (d) 45 sq cm
14. 14.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
15. 15.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 125 sq cm (c) 25 sq cm (d) 100 sq cm
16. 16.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 144 sq cm (c) 36 sq cm (d) 216 sq cm
17. 17.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
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
20. 20.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
21. 21.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
22. 22.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 10 cu cm (b) 146 cu cm (c) 90 cu cm (d) 16 cu cm
23. 23.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
24. 24.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 92 sq cm (b) 46 sq cm (c) 48 sq cm (d) 184 sq cm
25. 25.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
26. 26.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
27. 27.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
28. 28.A cuboid is 12 cm long, 8 cm wide and 7 cm high. What is its total surface area? (a) 672 sq cm (b) 944 sq cm (c) 472 sq cm (d) 236 sq cm
29. 29.A cuboid is 7 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 240 sq cm (b) 120 sq cm (c) 480 sq cm (d) 252 sq cm
30. 30.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 9 cu cm (c) 36 cu cm (d) 54 cu cm
31. 31.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
32. 32.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 6 cu cm (b) 54 cu cm (c) 14 cu cm (d) 102 cu cm
33. 33.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 324 sq cm (d) 729 sq cm
34. 34.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
35. 35.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 217 cu cm (c) 18 cu cm (d) 144 cu cm
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
37. 37.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 150 cu cm (c) 100 cu cm (d) 15 cu cm
38. 38.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
39. 39.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 30 cu cm (d) 400 cu cm
40. 40.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 84 sq cm (b) 21 sq cm (c) 18 sq cm (d) 42 sq cm

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