Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 311 · 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 area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
3. 3.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
4. 4.A cuboid is 7 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 524 sq cm (b) 131 sq cm (c) 280 sq cm (d) 262 sq cm
5. 5.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 100 sq cm (d) 600 sq cm
6. 6.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
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
8. 8.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) 8 times (c) 16 times (d) 64 times
9. 9.A cuboid is 5 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 202 cu cm (b) 20 cu cm (c) 18 cu cm (d) 180 cu cm
10. 10.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
11. 11.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 444 sq cm (b) 111 sq cm (c) 189 sq cm (d) 222 sq cm
12. 12.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
13. 13.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
14. 14.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
15. 15.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 324 sq cm (d) 729 sq cm
16. 16.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 10 cu cm (c) 20 cu cm (d) 9 cu cm
17. 17.A cuboid is 11 cm long, 10 cm wide and 3 cm high. What is its total surface area? (a) 173 sq cm (b) 692 sq cm (c) 346 sq cm (d) 330 sq cm
18. 18.A cuboid is 10 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 344 sq cm (b) 688 sq cm (c) 420 sq cm (d) 172 sq cm
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
20. 20.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
21. 21.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
22. 22.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 2 times (d) 8 times
23. 23.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) 16 times (c) 64 times (d) 8 times
24. 24.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
25. 25.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 27 cu cm (d) 729 cu cm
26. 26.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 68 sq cm (b) 80 sq cm (c) 136 sq cm (d) 272 sq cm
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
28. 28.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 76 sq cm (b) 40 sq cm (c) 152 sq cm (d) 38 sq cm
29. 29.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
30. 30.A cuboid is 11 cm long, 10 cm wide and 6 cm high. What is its total surface area? (a) 660 sq cm (b) 944 sq cm (c) 236 sq cm (d) 472 sq cm
31. 31.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
32. 32.A cuboid is 11 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 396 sq cm (b) 358 sq cm (c) 179 sq cm (d) 716 sq cm
33. 33.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
34. 34.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) 25 times (d) 5 times
35. 35.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
36. 36.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
37. 37.A cuboid is 8 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 232 sq cm (b) 224 sq cm (c) 116 sq cm (d) 464 sq cm
38. 38.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
39. 39.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 24 cu cm (d) 6 cu cm
40. 40.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm

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