Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 972 · 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 10 cm. What is its volume? (a) 400 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 600 cu cm
2. 2.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 324 cu cm (c) 486 cu cm (d) 27 cu cm
3. 3.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 36 sq cm (c) 9 sq cm (d) 27 sq cm
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
5. 5.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 4 sq cm (d) 24 sq cm
6. 6.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) 8 times (d) 64 times
7. 7.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 108 sq cm (b) 54 sq cm (c) 72 sq cm (d) 216 sq cm
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
9. 9.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 31 cu cm (b) 10 cu cm (c) 62 cu cm (d) 30 cu cm
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
11. 11.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 144 cu cm (c) 216 cu cm (d) 18 cu cm
12. 12.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
13. 13.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 6 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) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
15. 15.A cuboid is 12 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 432 cu cm (b) 25 cu cm (c) 384 cu cm (d) 108 cu cm
16. 16.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 512 cu cm (d) 256 cu cm
17. 17.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
18. 18.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) 2 times (c) 5 times (d) 4 times
19. 19.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) 6 times (c) 8 times (d) 4 times
20. 20.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
21. 21.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
23. 23.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 15 cu cm (b) 62 cu cm (c) 10 cu cm (d) 30 cu cm
24. 24.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 125 sq cm (d) 150 sq cm
25. 25.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
26. 26.A cuboid is 11 cm long, 7 cm wide and 7 cm high. What is its total surface area? (a) 406 sq cm (b) 203 sq cm (c) 812 sq cm (d) 539 sq cm
27. 27.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 97 sq cm (d) 96 sq cm
28. 28.A cuboid is 11 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 113 sq cm (b) 154 sq cm (c) 226 sq cm (d) 452 sq cm
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
30. 30.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
31. 31.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
33. 33.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) 8 times (c) 4 times (d) 16 times
34. 34.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 324 sq cm (b) 126 sq cm (c) 81 sq cm (d) 162 sq cm
35. 35.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
36. 36.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) 25 times (d) 125 times
37. 37.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) 64 times (c) 4 times (d) 8 times
38. 38.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 6 cu cm (d) 16 cu cm
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
40. 40.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 150 cu cm (d) 100 cu cm

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