Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 128 · 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 8 cm. What is its total surface area? (a) 64 sq cm (b) 512 sq cm (c) 256 sq cm (d) 384 sq cm
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
4. 4.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
5. 5.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) 4 times (d) 5 times
6. 6.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
7. 7.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
8. 8.A cuboid is 7 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 240 cu cm (b) 42 cu cm (c) 19 cu cm (d) 252 cu cm
9. 9.A cuboid is 6 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 472 sq cm (b) 118 sq cm (c) 236 sq cm (d) 240 sq cm
10. 10.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 24 cu cm (d) 256 cu cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
12. 12.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
13. 13.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
14. 14.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
15. 15.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
16. 16.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
17. 17.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 240 cu cm (b) 24 cu cm (c) 20 cu cm (d) 248 cu cm
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
19. 19.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 27 cu cm (c) 9 cu cm (d) 36 cu cm
20. 20.A cuboid is 9 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 27 cu cm (b) 15 cu cm (c) 81 cu cm (d) 126 cu cm
21. 21.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
22. 22.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) 16 times (d) 4 times
23. 23.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) 6 times (d) 3 times
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
25. 25.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 144 sq cm (d) 216 sq cm
26. 26.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
27. 27.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 11 cu cm (b) 80 cu cm (c) 48 cu cm (d) 12 cu cm
28. 28.A cuboid is 7 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 15 cu cm (b) 136 cu cm (c) 84 cu cm (d) 42 cu cm
29. 29.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 8 sq cm (c) 24 sq cm (d) 4 sq cm
30. 30.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) 25 times (c) 125 times (d) 10 times
31. 31.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
32. 32.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
33. 33.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
34. 34.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) 8 times (c) 5 times (d) 4 times
35. 35.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 90 sq cm (b) 252 sq cm (c) 126 sq cm (d) 63 sq cm
36. 36.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
37. 37.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) 8 times (c) 4 times (d) 2 times
38. 38.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
39. 39.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) 4 times (c) 64 times (d) 8 times
40. 40.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 726 sq cm (d) 1331 sq cm

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