Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 130 · 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 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
2. 2.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
3. 3.A cuboid is 7 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 13 cu cm (b) 21 cu cm (c) 102 cu cm (d) 63 cu cm
4. 4.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
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
6. 6.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 48 sq cm (b) 92 sq cm (c) 46 sq cm (d) 184 sq cm
7. 7.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) 6 times (c) 2 times (d) 8 times
8. 8.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 32 cu cm (b) 7 cu cm (c) 12 cu cm (d) 6 cu cm
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
11. 11.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
14. 14.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) 10 times (c) 125 times (d) 5 times
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
19. 19.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 64 cu cm (c) 96 cu cm (d) 65 cu cm
20. 20.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 196 sq cm (c) 343 sq cm (d) 294 sq cm
21. 21.If the side of a square 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
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) 3 times (d) 9 times
23. 23.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
24. 24.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 217 cu cm (d) 144 cu cm
25. 25.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 486 sq cm (c) 81 sq cm (d) 729 sq cm
26. 26.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
27. 27.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) 120 sq cm (d) 316 sq cm
28. 28.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
29. 29.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 48 cu cm (c) 88 cu cm (d) 8 cu cm
30. 30.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 400 cu cm
31. 31.A cuboid is 11 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 580 sq cm (b) 290 sq cm (c) 145 sq cm (d) 264 sq cm
32. 32.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
33. 33.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
34. 34.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
35. 35.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) 27 times (d) 3 times
36. 36.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 17 cu cm (b) 160 cu cm (c) 100 cu cm (d) 10 cu cm
37. 37.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 343 cu cm (d) 196 cu cm
38. 38.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 484 sq cm
39. 39.A cuboid is 7 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 138 sq cm (b) 552 sq cm (c) 280 sq cm (d) 276 sq cm
40. 40.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) 5 times (c) 25 times (d) 125 times

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