Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 573 · 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.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
2. 2.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
3. 3.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
4. 4.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
5. 5.A cuboid is 12 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 144 sq cm (b) 108 sq cm (c) 432 sq cm (d) 216 sq cm
6. 6.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 64 sq cm (b) 112 sq cm (c) 224 sq cm (d) 56 sq cm
7. 7.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
8. 8.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 486 cu cm (d) 324 cu cm
9. 9.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
10. 10.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
11. 11.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) 16 times (c) 64 times (d) 4 times
12. 12.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
13. 13.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
14. 14.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 55 sq cm (b) 75 sq cm (c) 110 sq cm (d) 220 sq cm
15. 15.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
16. 16.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 36 sq cm (c) 217 sq cm (d) 144 sq cm
17. 17.A cuboid is 12 cm long, 10 cm wide and 2 cm high. What is its total surface area? (a) 656 sq cm (b) 328 sq cm (c) 164 sq cm (d) 240 sq cm
18. 18.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
19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
20. 20.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 36 cu cm (d) 27 cu cm
21. 21.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
22. 22.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 576 cu cm (d) 36 cu cm
23. 23.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 96 sq cm (d) 97 sq cm
24. 24.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
25. 25.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 72 cu cm (b) 132 cu cm (c) 36 cu cm (d) 17 cu cm
26. 26.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
28. 28.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
29. 29.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) 4 times (d) 8 times
30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
31. 31.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 59 sq cm (b) 118 sq cm (c) 70 sq cm (d) 236 sq cm
32. 32.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
33. 33.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
34. 34.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
35. 35.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) 27 times (c) 6 times (d) 9 times
36. 36.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
37. 37.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) 5 times (c) 125 times (d) 10 times
38. 38.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 18 cu cm (c) 217 cu cm (d) 144 cu cm
39. 39.A cuboid is 7 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 280 sq cm (b) 262 sq cm (c) 131 sq cm (d) 524 sq cm
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm

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