Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 917 · 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, 2 cm wide and 10 cm high. What is its volume? (a) 8 cu cm (b) 136 cu cm (c) 16 cu cm (d) 80 cu cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
3. 3.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
4. 4.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
5. 5.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
6. 6.A cuboid is 9 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 202 cu cm (b) 36 cu cm (c) 180 cu cm (d) 18 cu cm
7. 7.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
8. 8.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
9. 9.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
10. 10.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
11. 11.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 54 sq cm (d) 36 sq cm
12. 12.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
13. 13.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 576 cu cm (c) 864 cu cm (d) 36 cu cm
14. 14.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 150 cu cm (d) 100 cu cm
15. 15.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
16. 16.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
17. 17.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 144 sq cm (d) 217 sq cm
18. 18.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
19. 19.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
20. 20.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
21. 21.A cuboid is 9 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 24 cu cm (b) 63 cu cm (c) 504 cu cm (d) 382 cu cm
22. 22.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 112 cu cm (b) 6 cu cm (c) 60 cu cm (d) 15 cu cm
23. 23.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
25. 25.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
26. 26.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
27. 27.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
28. 28.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) 8 times (d) 16 times
29. 29.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
30. 30.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
31. 31.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
32. 32.A cuboid is 12 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 216 sq cm (b) 576 sq cm (c) 432 sq cm (d) 864 sq cm
33. 33.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
34. 34.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 729 sq cm (d) 81 sq cm
35. 35.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
36. 36.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) 2 times (c) 8 times (d) 4 times
37. 37.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 26 sq cm (b) 52 sq cm (c) 24 sq cm (d) 104 sq cm
38. 38.A cuboid is 11 cm long, 10 cm wide and 5 cm high. What is its total surface area? (a) 860 sq cm (b) 550 sq cm (c) 215 sq cm (d) 430 sq cm
39. 39.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 6 cu cm (d) 16 cu cm
40. 40.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times

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