Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 314 · 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.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 65 cu cm (d) 96 cu cm
2. 2.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
3. 3.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
4. 4.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
5. 5.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
7. 7.A cuboid is 11 cm long, 8 cm wide and 6 cm high. What is its volume? (a) 25 cu cm (b) 404 cu cm (c) 88 cu cm (d) 528 cu cm
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
10. 10.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
11. 11.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
12. 12.A cuboid is 10 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 552 sq cm (b) 276 sq cm (c) 280 sq cm (d) 138 sq cm
13. 13.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 1728 sq cm (d) 144 sq cm
14. 14.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
15. 15.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
17. 17.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
18. 18.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 96 sq cm (d) 64 sq cm
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
20. 20.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
21. 21.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
22. 22.A cuboid is 9 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 150 cu cm (b) 36 cu cm (c) 108 cu cm (d) 16 cu cm
23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
24. 24.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 512 cu cm (d) 24 cu cm
25. 25.A cuboid is 10 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 320 sq cm (b) 100 sq cm (c) 80 sq cm (d) 160 sq cm
26. 26.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 8 cu cm (b) 52 cu cm (c) 24 cu cm (d) 9 cu cm
27. 27.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
29. 29.A cuboid is 10 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 60 cu cm (b) 480 cu cm (c) 376 cu cm (d) 24 cu cm
30. 30.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
31. 31.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
32. 32.A cuboid is 6 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 416 sq cm (b) 104 sq cm (c) 208 sq cm (d) 192 sq cm
33. 33.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) 5 times (c) 2 times (d) 4 times
34. 34.If the radius of a circle 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
35. 35.A cuboid is 8 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 48 sq cm (b) 184 sq cm (c) 46 sq cm (d) 92 sq cm
36. 36.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 486 cu cm (d) 324 cu cm
37. 37.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 59 sq cm (b) 236 sq cm (c) 70 sq cm (d) 118 sq cm
38. 38.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
39. 39.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) 8 times (c) 4 times (d) 64 times
40. 40.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times

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