Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 902 · 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 radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
3. 3.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
4. 4.A cuboid is 10 cm long, 9 cm wide and 4 cm high. What is its total surface area? (a) 332 sq cm (b) 664 sq cm (c) 166 sq cm (d) 360 sq cm
5. 5.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 126 cu cm (b) 15 cu cm (c) 14 cu cm (d) 90 cu cm
6. 6.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 600 sq cm (d) 100 sq cm
7. 7.A cuboid is 5 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 158 sq cm (b) 79 sq cm (c) 316 sq cm (d) 120 sq cm
8. 8.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 27 cu cm (d) 486 cu cm
9. 9.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) 64 times (c) 16 times (d) 8 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) 64 times (c) 8 times (d) 16 times
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
12. 12.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 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) 6 times (d) 4 times
15. 15.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
16. 16.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
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
18. 18.A cuboid is 12 cm long, 11 cm wide and 10 cm high. What is its total surface area? (a) 724 sq cm (b) 362 sq cm (c) 1320 sq cm (d) 1448 sq cm
19. 19.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
20. 20.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 217 sq cm (d) 36 sq cm
21. 21.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 90 cu cm (b) 146 cu cm (c) 18 cu cm (d) 16 cu cm
22. 22.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
23. 23.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
24. 24.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
25. 25.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
26. 26.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 726 sq cm (c) 1331 sq cm (d) 484 sq cm
27. 27.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 256 cu cm (d) 384 cu cm
28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
29. 29.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
30. 30.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
31. 31.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 76 sq cm (b) 152 sq cm (c) 40 sq cm (d) 38 sq cm
32. 32.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
33. 33.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
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
35. 35.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) 25 times (c) 10 times (d) 5 times
36. 36.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 144 sq cm (d) 1728 sq cm
37. 37.A cuboid is 10 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 216 sq cm (b) 180 sq cm (c) 432 sq cm (d) 108 sq cm
38. 38.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 11 cu cm (b) 76 cu cm (c) 8 cu cm (d) 40 cu cm
39. 39.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
40. 40.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 24 cu cm (d) 16 cu cm

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