Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 142 · 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 10 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 412 cu cm (b) 70 cu cm (c) 25 cu cm (d) 560 cu cm
2. 2.A cuboid is 8 cm long, 7 cm wide and 9 cm high. What is its volume? (a) 24 cu cm (b) 504 cu cm (c) 56 cu cm (d) 382 cu cm
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
4. 4.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 32 sq cm (d) 12 sq cm
5. 5.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
6. 6.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
7. 7.A cuboid is 8 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 240 sq cm (b) 268 sq cm (c) 536 sq cm (d) 134 sq cm
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
9. 9.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
10. 10.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 10 cu cm (b) 64 cu cm (c) 8 cu cm (d) 32 cu cm
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
13. 13.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) 64 times (c) 8 times (d) 4 times
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
15. 15.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 24 sq cm (d) 8 sq cm
16. 16.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
17. 17.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) 25 times (d) 10 times
18. 18.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 512 cu cm (d) 24 cu cm
19. 19.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) 5 times (c) 10 times (d) 125 times
20. 20.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
21. 21.A cuboid is 8 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 96 cu cm (b) 15 cu cm (c) 136 cu cm (d) 32 cu cm
22. 22.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 196 cu cm (d) 21 cu cm
23. 23.A cuboid is 9 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 664 sq cm (b) 332 sq cm (c) 360 sq cm (d) 166 sq cm
24. 24.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 486 cu cm (c) 324 cu cm (d) 27 cu cm
25. 25.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) 5 times (c) 4 times (d) 8 times
26. 26.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
27. 27.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
28. 28.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 54 sq cm (d) 9 sq cm
29. 29.A cuboid is 7 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 122 sq cm (b) 244 sq cm (c) 84 sq cm (d) 61 sq cm
30. 30.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 1728 sq cm (d) 144 sq cm
31. 31.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
32. 32.A cuboid is 10 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 30 cu cm (b) 294 cu cm (c) 22 cu cm (d) 270 cu cm
33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
34. 34.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
35. 35.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) 5 times (d) 25 times
36. 36.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
37. 37.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
38. 38.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 16 cu cm (d) 6 cu cm
39. 39.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
40. 40.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

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