Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 253 · 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 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 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) 2 times (b) 5 times (c) 8 times (d) 4 times
4. 4.A cuboid is 11 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 66 sq cm (b) 122 sq cm (c) 61 sq cm (d) 244 sq cm
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
7. 7.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
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
9. 9.If the radius of a circle 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
10. 10.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) 16 times (c) 8 times (d) 64 times
11. 11.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 1728 cu cm (c) 36 cu cm (d) 864 cu cm
12. 12.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 512 sq cm (d) 256 sq cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
14. 14.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 864 sq cm (c) 1728 sq cm (d) 576 sq cm
15. 15.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) 9 times (c) 3 times (d) 27 times
16. 16.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 196 sq cm (c) 343 sq cm (d) 49 sq cm
17. 17.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 324 sq cm (c) 486 sq cm (d) 729 sq cm
18. 18.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 55 sq cm (b) 220 sq cm (c) 75 sq cm (d) 110 sq cm
19. 19.A cuboid is 5 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 16 cu cm (b) 20 cu cm (c) 166 cu cm (d) 140 cu cm
20. 20.A cuboid is 10 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 50 cu cm (b) 300 cu cm (c) 21 cu cm (d) 280 cu cm
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
22. 22.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
23. 23.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 196 cu cm (c) 294 cu cm (d) 21 cu cm
24. 24.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
25. 25.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
26. 26.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
27. 27.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 20 sq cm (b) 24 sq cm (c) 96 sq cm (d) 48 sq cm
28. 28.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 25 sq cm (c) 150 sq cm (d) 125 sq cm
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
31. 31.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) 25 times (c) 125 times (d) 5 times
32. 32.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
33. 33.A cuboid is 12 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 208 sq cm (b) 832 sq cm (c) 416 sq cm (d) 480 sq cm
34. 34.A cuboid is 12 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 84 cu cm (b) 548 cu cm (c) 840 cu cm (d) 29 cu cm
35. 35.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
36. 36.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 6 cu cm (b) 30 cu cm (c) 10 cu cm (d) 62 cu cm
37. 37.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
38. 38.A cuboid is 9 cm long, 8 cm wide and 6 cm high. What is its total surface area? (a) 432 sq cm (b) 348 sq cm (c) 174 sq cm (d) 696 sq cm
39. 39.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
40. 40.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

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