Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 576 · 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 total surface area? (a) 400 sq cm (b) 600 sq cm (c) 100 sq cm (d) 1000 sq cm
2. 2.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 486 sq cm (d) 81 sq cm
3. 3.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 78 sq cm (b) 39 sq cm (c) 45 sq cm (d) 156 sq cm
4. 4.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) 4 times (c) 5 times (d) 2 times
5. 5.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
6. 6.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
7. 7.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
9. 9.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 216 cu cm (d) 217 cu cm
10. 10.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
11. 11.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
12. 12.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) 16 times (c) 4 times (d) 8 times
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
14. 14.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
16. 16.A cuboid is 6 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 168 sq cm (b) 108 sq cm (c) 336 sq cm (d) 84 sq cm
17. 17.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
18. 18.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 16 cu cm (d) 8 cu cm
19. 19.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
20. 20.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
21. 21.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
22. 22.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 11 cu cm (b) 76 cu cm (c) 10 cu cm (d) 40 cu cm
23. 23.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
25. 25.A cuboid is 11 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 148 cu cm (b) 88 cu cm (c) 17 cu cm (d) 22 cu cm
26. 26.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 256 sq cm (d) 64 sq cm
27. 27.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) 4 times (d) 8 times
28. 28.A cuboid is 10 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 70 cu cm (b) 208 cu cm (c) 19 cu cm (d) 140 cu cm
29. 29.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
30. 30.A cuboid is 12 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 252 sq cm (b) 141 sq cm (c) 282 sq cm (d) 564 sq cm
31. 31.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
32. 32.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
33. 33.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
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
35. 35.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
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
37. 37.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 726 sq cm (d) 484 sq cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 14 cu cm (b) 118 cu cm (c) 70 cu cm (d) 10 cu cm
39. 39.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
40. 40.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times

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