Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 640 · 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.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) 5 times (d) 4 times
2. 2.A cuboid is 7 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 636 sq cm (b) 159 sq cm (c) 318 sq cm (d) 378 sq cm
3. 3.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
4. 4.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
5. 5.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 343 sq cm (d) 196 sq cm
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
7. 7.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
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
9. 9.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 82 sq cm (b) 164 sq cm (c) 41 sq cm (d) 42 sq cm
10. 10.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 726 sq cm (c) 121 sq cm (d) 1331 sq cm
11. 11.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 18 cu cm (c) 144 cu cm (d) 217 cu cm
12. 12.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) 25 times (c) 125 times (d) 10 times
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
14. 14.A cuboid is 6 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 176 sq cm (b) 48 sq cm (c) 88 sq cm (d) 44 sq cm
15. 15.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 100 cu cm (b) 13 cu cm (c) 8 cu cm (d) 56 cu cm
16. 16.A cuboid is 7 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 116 sq cm (b) 224 sq cm (c) 232 sq cm (d) 464 sq cm
17. 17.A cuboid is 8 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 144 sq cm (b) 360 sq cm (c) 90 sq cm (d) 180 sq cm
18. 18.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
20. 20.A cuboid is 12 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 672 sq cm (b) 472 sq cm (c) 944 sq cm (d) 236 sq cm
21. 21.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 104 sq cm (b) 26 sq cm (c) 52 sq cm (d) 24 sq cm
22. 22.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 30 cu cm (d) 1000 cu cm
23. 23.A cuboid is 7 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 532 sq cm (b) 133 sq cm (c) 294 sq cm (d) 266 sq cm
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
25. 25.A cuboid is 9 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 378 sq cm (b) 756 sq cm (c) 189 sq cm (d) 486 sq cm
26. 26.A cuboid is 9 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 45 cu cm (b) 16 cu cm (c) 90 cu cm (d) 146 cu cm
27. 27.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
28. 28.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
29. 29.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
31. 31.A cuboid is 8 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 240 sq cm (b) 236 sq cm (c) 118 sq cm (d) 472 sq cm
32. 32.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) 6 times (c) 3 times (d) 27 times
33. 33.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) 8 times (c) 2 times (d) 4 times
34. 34.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
35. 35.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 120 cu cm (b) 148 cu cm (c) 20 cu cm (d) 15 cu cm
36. 36.A cuboid is 7 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 189 cu cm (b) 222 cu cm (c) 19 cu cm (d) 21 cu cm
37. 37.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) 3 times (d) 6 times
38. 38.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
39. 39.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
40. 40.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm

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