Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 55 · 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 area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
2. 2.A cuboid is 10 cm long, 9 cm wide and 3 cm high. What is its total surface area? (a) 147 sq cm (b) 270 sq cm (c) 588 sq cm (d) 294 sq cm
3. 3.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) 2 times (d) 4 times
4. 4.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
5. 5.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 294 sq cm (d) 196 sq cm
6. 6.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
7. 7.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
9. 9.A cuboid is 11 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 198 cu cm (b) 99 cu cm (c) 22 cu cm (d) 278 cu cm
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
12. 12.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 100 sq cm (d) 600 sq cm
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
14. 14.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 8 times (c) 4 times (d) 6 times
15. 15.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) 27 times (c) 6 times (d) 9 times
16. 16.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 62 cu cm (b) 10 cu cm (c) 30 cu cm (d) 15 cu cm
17. 17.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
19. 19.A cuboid is 10 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 294 cu cm (b) 22 cu cm (c) 30 cu cm (d) 270 cu cm
20. 20.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) 3 times (d) 9 times
21. 21.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
22. 22.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 16 sq cm (d) 64 sq cm
23. 23.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 576 cu cm (d) 1728 cu cm
24. 24.A cuboid is 7 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 28 cu cm (b) 166 cu cm (c) 140 cu cm (d) 16 cu cm
25. 25.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 42 cu cm (c) 82 cu cm (d) 14 cu cm
26. 26.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 81 sq cm (c) 729 sq cm (d) 324 sq cm
27. 27.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) 5 times (c) 10 times (d) 25 times
28. 28.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
30. 30.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
31. 31.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) 64 times (d) 8 times
32. 32.A cuboid is 10 cm long, 8 cm wide and 6 cm high. What is its volume? (a) 376 cu cm (b) 480 cu cm (c) 24 cu cm (d) 80 cu cm
33. 33.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
34. 34.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 14 cu cm (b) 84 cu cm (c) 122 cu cm (d) 12 cu cm
35. 35.A cuboid is 12 cm long, 8 cm wide and 4 cm high. What is its total surface area? (a) 176 sq cm (b) 704 sq cm (c) 352 sq cm (d) 384 sq cm
36. 36.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
37. 37.A cuboid is 11 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 66 cu cm (b) 330 cu cm (c) 302 cu cm (d) 22 cu cm
38. 38.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
39. 39.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
40. 40.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm

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