Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 344 · 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 radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
2. 2.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 96 cu cm (d) 64 cu cm
3. 3.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
4. 4.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
5. 5.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 25 sq cm (d) 150 sq cm
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
7. 7.A cuboid is 9 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 208 sq cm (b) 832 sq cm (c) 416 sq cm (d) 576 sq cm
8. 8.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) 8 times (c) 4 times (d) 5 times
9. 9.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 32 sq cm (b) 16 sq cm (c) 12 sq cm (d) 64 sq cm
10. 10.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
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.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
13. 13.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 24 cu cm (d) 256 cu cm
14. 14.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) 8 times (c) 64 times (d) 16 times
15. 15.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 76 sq cm (b) 152 sq cm (c) 96 sq cm (d) 304 sq cm
16. 16.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
19. 19.A cuboid is 5 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 180 sq cm (b) 202 sq cm (c) 404 sq cm (d) 101 sq cm
20. 20.A cuboid is 6 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 14 cu cm (b) 90 cu cm (c) 126 cu cm (d) 30 cu cm
21. 21.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 6 cu cm (d) 16 cu cm
22. 22.A cuboid is 6 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 136 sq cm (b) 272 sq cm (c) 68 sq cm (d) 84 sq cm
23. 23.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 600 cu cm (d) 400 cu cm
24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
25. 25.A cuboid is 8 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 46 sq cm (b) 92 sq cm (c) 184 sq cm (d) 48 sq cm
26. 26.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
27. 27.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
28. 28.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) 10 times (c) 25 times (d) 5 times
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
30. 30.A cuboid is 8 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 36 sq cm (b) 72 sq cm (c) 144 sq cm (d) 32 sq cm
31. 31.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 20 cu cm (b) 200 cu cm (c) 220 cu cm (d) 19 cu cm
32. 32.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
33. 33.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
34. 34.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) 3 times (c) 27 times (d) 9 times
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
36. 36.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) 2 times (c) 6 times (d) 8 times
37. 37.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
38. 38.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
39. 39.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 96 sq cm (d) 97 sq cm
40. 40.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times

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