Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 137 · 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 11 cm. What is its volume? (a) 726 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 484 cu cm
2. 2.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
3. 3.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) 5 times (c) 8 times (d) 4 times
4. 4.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
5. 5.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
7. 7.A cuboid is 11 cm long, 9 cm wide and 6 cm high. What is its volume? (a) 99 cu cm (b) 438 cu cm (c) 26 cu cm (d) 594 cu cm
8. 8.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
9. 9.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
11. 11.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
12. 12.A cuboid is 6 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 384 sq cm (b) 96 sq cm (c) 192 sq cm (d) 180 sq cm
13. 13.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
15. 15.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 486 sq cm (c) 81 sq cm (d) 324 sq cm
16. 16.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 18 cu cm (b) 150 cu cm (c) 190 cu cm (d) 15 cu cm
17. 17.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 27 cu cm (d) 36 cu cm
18. 18.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) 6 times (d) 3 times
19. 19.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
20. 20.A cuboid is 12 cm long, 8 cm wide and 7 cm high. What is its volume? (a) 96 cu cm (b) 672 cu cm (c) 472 cu cm (d) 27 cu cm
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
22. 22.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
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
24. 24.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
25. 25.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
26. 26.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
27. 27.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) 10 times (c) 5 times (d) 125 times
28. 28.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
29. 29.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 36 sq cm (d) 27 sq cm
30. 30.A cuboid is 6 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 428 sq cm (b) 107 sq cm (c) 214 sq cm (d) 210 sq cm
31. 31.A cuboid is 9 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 764 sq cm (b) 382 sq cm (c) 191 sq cm (d) 504 sq cm
32. 32.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 196 sq cm (d) 294 sq cm
33. 33.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 729 cu cm (d) 27 cu cm
34. 34.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
35. 35.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 26 sq cm (b) 24 sq cm (c) 52 sq cm (d) 104 sq cm
36. 36.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 82 sq cm (b) 42 sq cm (c) 41 sq cm (d) 164 sq cm
37. 37.A cuboid is 7 cm long, 6 cm wide and 9 cm high. What is its volume? (a) 42 cu cm (b) 318 cu cm (c) 22 cu cm (d) 378 cu cm
38. 38.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 75 sq cm (b) 108 sq cm (c) 300 sq cm (d) 150 sq cm
39. 39.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 144 cu cm (d) 217 cu cm
40. 40.A cuboid is 7 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 19 cu cm (b) 28 cu cm (c) 232 cu cm (d) 224 cu cm

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