Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 671 · 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 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) 64 times (d) 4 times
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
4. 4.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) 5 times (c) 125 times (d) 25 times
5. 5.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
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
7. 7.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
8. 8.A cuboid is 11 cm long, 8 cm wide and 10 cm high. What is its total surface area? (a) 278 sq cm (b) 556 sq cm (c) 1112 sq cm (d) 880 sq cm
9. 9.A cuboid is 7 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 91 sq cm (b) 182 sq cm (c) 364 sq cm (d) 147 sq cm
10. 10.A cuboid is 11 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 113 sq cm (b) 154 sq cm (c) 226 sq cm (d) 452 sq cm
11. 11.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) 9 times (c) 6 times (d) 27 times
12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
13. 13.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) 2 times (c) 4 times (d) 8 times
14. 14.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
15. 15.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
16. 16.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) 4 times (c) 8 times (d) 5 times
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
18. 18.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
19. 19.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) 125 times (c) 5 times (d) 10 times
20. 20.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
21. 21.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 132 sq cm (b) 36 sq cm (c) 33 sq cm (d) 66 sq cm
22. 22.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
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
24. 24.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
25. 25.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
26. 26.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
28. 28.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
29. 29.A cuboid is 9 cm long, 7 cm wide and 10 cm high. What is its total surface area? (a) 446 sq cm (b) 892 sq cm (c) 630 sq cm (d) 223 sq cm
30. 30.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
31. 31.A cuboid is 6 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 84 sq cm (b) 68 sq cm (c) 272 sq cm (d) 136 sq cm
32. 32.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 100 sq cm (c) 600 sq cm (d) 1000 sq cm
33. 33.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 36 cu cm (d) 576 cu cm
34. 34.A cuboid is 11 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 524 sq cm (b) 131 sq cm (c) 231 sq cm (d) 262 sq cm
35. 35.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) 3 times (c) 27 times (d) 9 times
36. 36.A cuboid is 11 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 330 sq cm (b) 346 sq cm (c) 173 sq cm (d) 692 sq cm
37. 37.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
38. 38.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) 5 times (c) 4 times (d) 8 times
39. 39.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 54 cu cm (d) 36 cu cm
40. 40.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) 8 times (c) 64 times (d) 16 times

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