Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 427 · 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 cuboid is 9 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 216 sq cm (b) 123 sq cm (c) 492 sq cm (d) 246 sq cm
2. 2.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
3. 3.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 2 times (d) 6 times
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
5. 5.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) 64 times (c) 4 times (d) 8 times
6. 6.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
7. 7.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
8. 8.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 16 sq cm (d) 97 sq cm
9. 9.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 294 sq cm (c) 196 sq cm (d) 343 sq cm
10. 10.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
11. 11.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) 25 times (c) 10 times (d) 5 times
12. 12.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
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
14. 14.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
15. 15.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
17. 17.A cuboid is 8 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 158 cu cm (b) 16 cu cm (c) 24 cu cm (d) 120 cu cm
18. 18.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) 25 times (d) 10 times
19. 19.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 112 sq cm (b) 224 sq cm (c) 60 sq cm (d) 56 sq cm
20. 20.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) 4 times (d) 64 times
21. 21.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
22. 22.A cuboid is 12 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 252 cu cm (b) 216 cu cm (c) 21 cu cm (d) 36 cu cm
23. 23.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
25. 25.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
26. 26.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
27. 27.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 486 sq cm (d) 324 sq cm
28. 28.A cuboid is 10 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 880 sq cm (b) 220 sq cm (c) 440 sq cm (d) 600 sq cm
29. 29.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 14 cu cm (b) 82 cu cm (c) 12 cu cm (d) 42 cu cm
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
31. 31.A cuboid is 12 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 108 cu cm (b) 552 cu cm (c) 29 cu cm (d) 864 cu cm
32. 32.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 152 sq cm (b) 40 sq cm (c) 38 sq cm (d) 76 sq cm
33. 33.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 188 sq cm (b) 60 sq cm (c) 94 sq cm (d) 47 sq cm
34. 34.A cuboid is 11 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 268 cu cm (b) 66 cu cm (c) 21 cu cm (d) 264 cu cm
35. 35.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 1000 sq cm (c) 400 sq cm (d) 100 sq cm
36. 36.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
37. 37.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 256 cu cm (d) 512 cu cm
38. 38.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 8 sq cm (c) 16 sq cm (d) 24 sq cm
39. 39.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm

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