Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 578 · 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 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 122 cu cm (c) 14 cu cm (d) 84 cu cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 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) 4 times (b) 8 times (c) 6 times (d) 2 times
4. 4.A cuboid is 12 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 60 cu cm (b) 392 cu cm (c) 25 cu cm (d) 480 cu cm
5. 5.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 6 cu cm (b) 42 cu cm (c) 12 cu cm (d) 82 cu cm
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
7. 7.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
9. 9.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 484 cu cm (c) 33 cu cm (d) 726 cu cm
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
11. 11.A cuboid is 9 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 508 sq cm (b) 252 sq cm (c) 254 sq cm (d) 127 sq cm
12. 12.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
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
14. 14.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 216 sq cm (c) 217 sq cm (d) 36 sq cm
15. 15.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 64 sq cm (c) 16 sq cm (d) 96 sq cm
16. 16.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
17. 17.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
18. 18.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) 64 times (c) 8 times (d) 16 times
19. 19.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
20. 20.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
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
22. 22.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
23. 23.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
24. 24.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
25. 25.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 180 sq cm (b) 108 sq cm (c) 216 sq cm (d) 432 sq cm
26. 26.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
27. 27.A cuboid is 10 cm long, 9 cm wide and 10 cm high. What is its volume? (a) 900 cu cm (b) 29 cu cm (c) 560 cu cm (d) 90 cu cm
28. 28.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 150 sq cm (d) 100 sq cm
29. 29.A cuboid is 7 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 111 sq cm (b) 222 sq cm (c) 444 sq cm (d) 189 sq cm
30. 30.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 72 sq cm (b) 62 sq cm (c) 124 sq cm (d) 248 sq cm
31. 31.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
32. 32.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
33. 33.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 30 sq cm (b) 62 sq cm (c) 124 sq cm (d) 31 sq cm
34. 34.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 27 cu cm (c) 9 cu cm (d) 36 cu cm
35. 35.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
36. 36.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
37. 37.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
38. 38.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 6 cu cm (d) 8 cu cm
39. 39.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
40. 40.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm

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