Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 848 · 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 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
3. 3.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
5. 5.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 576 cu cm
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
7. 7.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
8. 8.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 2 times (d) 6 times
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
10. 10.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
11. 11.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
12. 12.A cuboid is 10 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 20 cu cm (b) 50 cu cm (c) 250 cu cm (d) 251 cu cm
13. 13.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
14. 14.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
15. 15.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 512 cu cm (c) 256 cu cm (d) 24 cu cm
16. 16.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
17. 17.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
18. 18.A cuboid is 10 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 164 sq cm (b) 82 sq cm (c) 120 sq cm (d) 328 sq cm
19. 19.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) 27 times (d) 6 times
20. 20.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
21. 21.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
23. 23.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
24. 24.If the side of a square 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
25. 25.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 600 sq cm (c) 1000 sq cm (d) 400 sq cm
26. 26.A cuboid is 7 cm long, 6 cm wide and 9 cm high. What is its volume? (a) 42 cu cm (b) 318 cu cm (c) 378 cu cm (d) 22 cu cm
27. 27.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 486 sq cm (d) 324 sq cm
28. 28.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 9 cu cm (b) 12 cu cm (c) 52 cu cm (d) 24 cu cm
29. 29.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
30. 30.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
31. 31.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 8 sq cm (d) 4 sq cm
32. 32.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
33. 33.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
34. 34.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) 9 times (c) 27 times (d) 6 times
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
36. 36.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
37. 37.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 80 sq cm (b) 100 sq cm (c) 320 sq cm (d) 160 sq cm
38. 38.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) 5 times (c) 4 times (d) 2 times
39. 39.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 54 sq cm (b) 51 sq cm (c) 102 sq cm (d) 204 sq cm
40. 40.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm

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