Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 949 · 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 8 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 280 cu cm (b) 40 cu cm (c) 20 cu cm (d) 262 cu cm
2. 2.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
6. 6.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
7. 7.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) 16 times (c) 64 times (d) 8 times
8. 8.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 36 cu cm (d) 54 cu cm
9. 9.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
10. 10.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 486 sq cm (d) 81 sq cm
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
12. 12.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
13. 13.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
14. 14.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 144 sq cm
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
16. 16.A cuboid is 8 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 240 cu cm (b) 48 cu cm (c) 19 cu cm (d) 236 cu cm
17. 17.A cuboid is 8 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 236 sq cm (b) 472 sq cm (c) 240 sq cm (d) 118 sq cm
18. 18.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) 25 times (c) 10 times (d) 5 times
19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
20. 20.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 256 cu cm (c) 384 cu cm (d) 512 cu cm
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
22. 22.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
24. 24.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
25. 25.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) 8 times (c) 64 times (d) 16 times
26. 26.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 484 sq cm
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
28. 28.A cuboid is 7 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 214 cu cm (b) 35 cu cm (c) 18 cu cm (d) 210 cu cm
29. 29.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 112 sq cm (b) 56 sq cm (c) 224 sq cm (d) 60 sq cm
30. 30.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) 3 times (c) 6 times (d) 27 times
31. 31.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
32. 32.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) 8 times (c) 2 times (d) 4 times
33. 33.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 52 cu cm (b) 6 cu cm (c) 24 cu cm (d) 9 cu cm
34. 34.A cuboid is 9 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 684 sq cm (b) 405 sq cm (c) 342 sq cm (d) 171 sq cm
35. 35.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 217 sq cm (d) 216 sq cm
36. 36.A cuboid is 11 cm long, 8 cm wide and 2 cm high. What is its total surface area? (a) 126 sq cm (b) 504 sq cm (c) 252 sq cm (d) 176 sq cm
37. 37.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
38. 38.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
39. 39.A cuboid is 12 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 48 cu cm (b) 224 cu cm (c) 20 cu cm (d) 192 cu cm
40. 40.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm

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