Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 79 · 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 diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
2. 2.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) 5 times (c) 4 times (d) 2 times
3. 3.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) 27 times (c) 3 times (d) 6 times
4. 4.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
6. 6.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
7. 7.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
8. 8.A cuboid is 10 cm long, 8 cm wide and 2 cm high. What is its total surface area? (a) 160 sq cm (b) 232 sq cm (c) 116 sq cm (d) 464 sq cm
9. 9.A cuboid is 11 cm long, 9 cm wide and 5 cm high. What is its volume? (a) 495 cu cm (b) 398 cu cm (c) 25 cu cm (d) 99 cu cm
10. 10.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
12. 12.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
13. 13.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
16. 16.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 343 sq cm (d) 196 sq cm
17. 17.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
18. 18.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
19. 19.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
20. 20.A cuboid is 7 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 21 cu cm (b) 280 cu cm (c) 28 cu cm (d) 276 cu cm
21. 21.A cuboid is 11 cm long, 10 cm wide and 8 cm high. What is its total surface area? (a) 278 sq cm (b) 880 sq cm (c) 1112 sq cm (d) 556 sq cm
22. 22.A cuboid is 9 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 14 cu cm (b) 102 cu cm (c) 54 cu cm (d) 18 cu cm
23. 23.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
24. 24.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
25. 25.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 216 sq cm (c) 36 sq cm (d) 217 sq cm
26. 26.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
27. 27.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 44 sq cm (b) 88 sq cm (c) 176 sq cm (d) 48 sq cm
28. 28.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
29. 29.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) 9 times (c) 27 times (d) 3 times
30. 30.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 56 sq cm (b) 200 sq cm (c) 100 sq cm (d) 50 sq cm
31. 31.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
32. 32.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 217 cu cm (d) 216 cu cm
33. 33.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
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.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
36. 36.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
37. 37.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 384 cu cm (d) 256 cu cm
38. 38.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
39. 39.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 8 sq cm (c) 16 sq cm (d) 4 sq cm
40. 40.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 100 sq cm (c) 150 sq cm (d) 25 sq cm

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