Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 127 · 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 cuboid is 10 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 50 cu cm (b) 400 cu cm (c) 500 cu cm (d) 25 cu cm
2. 2.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
3. 3.A cuboid is 11 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 430 cu cm (b) 26 cu cm (c) 550 cu cm (d) 55 cu cm
4. 4.A cuboid is 5 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 79 sq cm (b) 316 sq cm (c) 120 sq cm (d) 158 sq cm
5. 5.A cuboid is 5 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 180 cu cm (b) 18 cu cm (c) 20 cu cm (d) 202 cu cm
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
7. 7.A cuboid is 10 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 20 cu cm (b) 208 cu cm (c) 19 cu cm (d) 140 cu cm
8. 8.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) 125 times (c) 5 times (d) 10 times
9. 9.A cuboid is 10 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 120 cu cm (b) 40 cu cm (c) 164 cu cm (d) 17 cu cm
10. 10.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 54 sq cm (d) 9 sq cm
11. 11.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 343 cu cm (d) 21 cu cm
12. 12.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 512 cu cm (c) 24 cu cm (d) 256 cu cm
13. 13.A cuboid is 6 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 108 cu cm (b) 18 cu cm (c) 15 cu cm (d) 144 cu cm
14. 14.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) 5 times (c) 4 times (d) 8 times
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
17. 17.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
19. 19.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
20. 20.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
21. 21.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
22. 22.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
23. 23.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
24. 24.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) 9 times (d) 3 times
25. 25.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 864 sq cm
26. 26.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
27. 27.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 180 sq cm (b) 50 sq cm (c) 45 sq cm (d) 90 sq cm
28. 28.A cuboid is 11 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 24 cu cm (b) 396 cu cm (c) 358 cu cm (d) 99 cu cm
29. 29.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
30. 30.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 726 sq cm (d) 1331 sq cm
31. 31.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) 5 times (c) 10 times (d) 25 times
32. 32.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
33. 33.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
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
35. 35.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 16 sq cm (d) 64 sq cm
36. 36.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 144 sq cm (d) 217 sq cm
37. 37.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
38. 38.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 196 sq cm (d) 294 sq cm
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
40. 40.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) 8 times (c) 16 times (d) 64 times

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