Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 71 · 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) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
2. 2.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
3. 3.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 30 cu cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
7. 7.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 64 sq cm (c) 16 sq cm (d) 96 sq cm
8. 8.A cuboid is 6 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 336 sq cm (b) 84 sq cm (c) 144 sq cm (d) 168 sq cm
9. 9.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
10. 10.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
11. 11.A cuboid is 8 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 13 cu cm (c) 24 cu cm (d) 92 cu cm
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
13. 13.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 400 sq cm (c) 100 sq cm (d) 1000 sq cm
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
15. 15.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) 64 times (d) 8 times
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
17. 17.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 48 sq cm (b) 40 sq cm (c) 80 sq cm (d) 160 sq cm
18. 18.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) 4 times (c) 8 times (d) 5 times
19. 19.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) 5 times (d) 4 times
20. 20.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 486 sq cm (c) 81 sq cm (d) 324 sq cm
21. 21.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 18 cu cm (b) 17 cu cm (c) 144 cu cm (d) 180 cu cm
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
23. 23.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
24. 24.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
25. 25.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 36 sq cm (c) 27 sq cm (d) 54 sq cm
26. 26.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
28. 28.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 6 cu cm (d) 24 cu cm
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
30. 30.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
31. 31.A cuboid is 10 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 400 cu cm (b) 50 cu cm (c) 25 cu cm (d) 500 cu cm
32. 32.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) 2 times (c) 8 times (d) 4 times
33. 33.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 65 sq cm (b) 128 sq cm (c) 64 sq cm (d) 32 sq cm
34. 34.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
36. 36.A cuboid is 8 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 101 sq cm (b) 202 sq cm (c) 168 sq cm (d) 404 sq cm
37. 37.A cuboid is 8 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 114 sq cm (b) 72 sq cm (c) 57 sq cm (d) 228 sq cm
38. 38.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 136 sq cm (b) 80 sq cm (c) 68 sq cm (d) 272 sq cm
39. 39.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) 16 times (c) 8 times (d) 64 times
40. 40.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

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