Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 586 · 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.If the side of a square 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
2. 2.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
3. 3.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 320 sq cm (b) 80 sq cm (c) 160 sq cm (d) 100 sq cm
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
6. 6.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
7. 7.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) 2 times (d) 6 times
8. 8.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
10. 10.A cuboid is 6 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 14 cu cm (b) 18 cu cm (c) 90 cu cm (d) 126 cu cm
11. 11.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
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
13. 13.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 9 cu cm (b) 48 cu cm (c) 10 cu cm (d) 20 cu cm
14. 14.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 144 sq cm
15. 15.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
16. 16.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 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) 125 times (b) 25 times (c) 5 times (d) 10 times
18. 18.A cuboid is 10 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 92 sq cm (b) 368 sq cm (c) 184 sq cm (d) 120 sq cm
19. 19.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 21 cu cm (d) 196 cu cm
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
23. 23.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
25. 25.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
26. 26.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
27. 27.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
28. 28.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 11 cu cm (b) 36 cu cm (c) 18 cu cm (d) 72 cu cm
29. 29.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 64 cu cm (c) 65 cu cm (d) 96 cu cm
30. 30.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) 4 times (c) 16 times (d) 64 times
31. 31.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
32. 32.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 11 cu cm (b) 12 cu cm (c) 36 cu cm (d) 72 cu cm
33. 33.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
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
35. 35.A cuboid is 8 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 160 cu cm (b) 20 cu cm (c) 232 cu cm (d) 16 cu cm
36. 36.A cuboid is 9 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 108 sq cm (b) 150 sq cm (c) 300 sq cm (d) 75 sq cm
37. 37.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
38. 38.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
39. 39.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 126 cu cm (b) 190 cu cm (c) 18 cu cm (d) 127 cu cm
40. 40.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm

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