Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 906 · 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.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
2. 2.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 726 cu cm
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
5. 5.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 112 sq cm (b) 64 sq cm (c) 56 sq cm (d) 224 sq cm
6. 6.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 15 cu cm (d) 100 cu cm
7. 7.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
8. 8.A cuboid is 10 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 268 sq cm (b) 134 sq cm (c) 240 sq cm (d) 536 sq cm
9. 9.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
12. 12.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 384 cu cm (d) 256 cu cm
13. 13.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
14. 14.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) 4 times (c) 8 times (d) 16 times
15. 15.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
16. 16.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 217 sq cm (c) 144 sq cm (d) 36 sq cm
17. 17.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) 4 times (c) 6 times (d) 8 times
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
19. 19.A cuboid is 9 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 20 cu cm (b) 254 cu cm (c) 252 cu cm (d) 63 cu cm
20. 20.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
21. 21.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 512 sq cm (c) 256 sq cm (d) 64 sq 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) 4 times (d) 2 times
23. 23.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) 125 times (c) 5 times (d) 10 times
24. 24.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 96 cu cm (d) 12 cu cm
25. 25.A cuboid is 9 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 230 sq cm (b) 115 sq cm (c) 460 sq cm (d) 225 sq cm
26. 26.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
27. 27.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
28. 28.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 729 cu cm (d) 486 cu cm
29. 29.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
30. 30.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) 4 times (c) 64 times (d) 16 times
31. 31.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
32. 32.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
33. 33.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
34. 34.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
35. 35.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 6 cu cm (d) 24 cu cm
36. 36.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 864 cu cm (d) 1728 cu cm
37. 37.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
38. 38.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) 5 times (c) 10 times (d) 25 times
39. 39.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 6 cu cm (b) 82 cu cm (c) 12 cu cm (d) 42 cu cm
40. 40.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm

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