Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 896 · 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 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
2. 2.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
4. 4.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
6. 6.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) 4 times (c) 8 times (d) 6 times
7. 7.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 486 sq cm (d) 81 sq cm
8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
9. 9.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
12. 12.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 33 cu cm
13. 13.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) 3 times (c) 27 times (d) 9 times
14. 14.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
15. 15.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
16. 16.A cuboid is 8 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 272 sq cm (b) 96 sq cm (c) 136 sq cm (d) 68 sq cm
17. 17.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
19. 19.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
20. 20.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
21. 21.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
22. 22.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) 5 times (d) 8 times
23. 23.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 217 sq cm (c) 144 sq cm (d) 36 sq cm
24. 24.A cuboid is 8 cm long, 7 cm wide and 9 cm high. What is its total surface area? (a) 382 sq cm (b) 504 sq cm (c) 191 sq cm (d) 764 sq cm
25. 25.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
26. 26.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) 64 times (c) 8 times (d) 4 times
27. 27.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 484 sq cm (c) 121 sq cm (d) 726 sq cm
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 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) 132 sq cm (d) 1386 sq cm
30. 30.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
31. 31.A cuboid is 7 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 13 cu cm (b) 102 cu cm (c) 63 cu cm (d) 21 cu 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) 2 times (b) 8 times (c) 5 times (d) 4 times
33. 33.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
34. 34.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
35. 35.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
36. 36.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
37. 37.A cuboid is 12 cm long, 7 cm wide and 5 cm high. What is its total surface area? (a) 179 sq cm (b) 358 sq cm (c) 420 sq cm (d) 716 sq cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 90 cu cm (b) 146 cu cm (c) 10 cu cm (d) 16 cu cm
39. 39.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 27 cu cm (d) 54 cu cm
40. 40.A cuboid is 12 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 256 cu cm (b) 60 cu cm (c) 240 cu cm (d) 21 cu cm

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