Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 62 · 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.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
2. 2.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
4. 4.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
5. 5.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
6. 6.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) 4 times (d) 16 times
7. 7.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 21 cu cm (d) 343 cu cm
8. 8.A cuboid is 11 cm long, 9 cm wide and 10 cm high. What is its total surface area? (a) 1196 sq cm (b) 299 sq cm (c) 598 sq cm (d) 990 sq cm
9. 9.A cuboid is 12 cm long, 8 cm wide and 5 cm high. What is its total surface area? (a) 392 sq cm (b) 480 sq cm (c) 784 sq cm (d) 196 sq cm
10. 10.A cuboid is 8 cm long, 7 cm wide and 10 cm high. What is its total surface area? (a) 412 sq cm (b) 560 sq cm (c) 206 sq cm (d) 824 sq cm
11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
12. 12.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
13. 13.A cuboid is 12 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 504 sq cm (b) 198 sq cm (c) 792 sq cm (d) 396 sq cm
14. 14.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 144 cu cm (c) 18 cu cm (d) 216 cu cm
15. 15.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 76 sq cm (b) 304 sq cm (c) 152 sq cm (d) 96 sq cm
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
17. 17.A cuboid is 10 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 640 sq cm (b) 320 sq cm (c) 300 sq cm (d) 160 sq cm
18. 18.A cuboid is 9 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 248 sq cm (b) 62 sq cm (c) 72 sq cm (d) 124 sq cm
19. 19.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
20. 20.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 726 sq cm (c) 121 sq cm (d) 484 sq cm
21. 21.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
22. 22.A cuboid is 8 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 32 cu cm (b) 15 cu cm (c) 136 cu cm (d) 96 cu cm
23. 23.A cuboid is 9 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 212 cu cm (b) 18 cu cm (c) 144 cu cm (d) 19 cu cm
24. 24.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
25. 25.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) 10 times (c) 5 times (d) 125 times
26. 26.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
27. 27.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) 125 times (c) 25 times (d) 10 times
28. 28.A cuboid is 9 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 124 cu cm (b) 15 cu cm (c) 36 cu cm (d) 72 cu cm
29. 29.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
30. 30.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 486 sq cm (d) 324 sq cm
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
32. 32.A cuboid is 11 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 330 cu cm (b) 55 cu cm (c) 22 cu cm (d) 302 cu cm
33. 33.A cuboid is 6 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 210 sq cm (b) 428 sq cm (c) 107 sq cm (d) 214 sq cm
34. 34.A cuboid is 6 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 472 sq cm (b) 240 sq cm (c) 236 sq cm (d) 118 sq cm
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
37. 37.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 18 cu cm (b) 72 cu cm (c) 36 cu cm (d) 11 cu cm
38. 38.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
39. 39.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
40. 40.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 72 cu cm (b) 11 cu cm (c) 6 cu cm (d) 36 cu cm

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