Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 604 · 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 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
2. 2.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
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
4. 4.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
5. 5.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
6. 6.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 196 cu cm (c) 21 cu cm (d) 294 cu cm
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
8. 8.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
9. 9.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 90 cu cm (b) 18 cu cm (c) 12 cu cm (d) 54 cu cm
10. 10.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 12 cu cm (d) 64 cu cm
11. 11.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 576 sq cm
12. 12.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
13. 13.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
14. 14.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 152 cu cm (b) 12 cu cm (c) 16 cu cm (d) 96 cu cm
15. 15.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 2 times (d) 8 times
17. 17.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
18. 18.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) 125 times (c) 5 times (d) 10 times
19. 19.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
23. 23.A cuboid is 12 cm long, 9 cm wide and 7 cm high. What is its total surface area? (a) 255 sq cm (b) 1020 sq cm (c) 756 sq cm (d) 510 sq cm
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
25. 25.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
27. 27.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 160 sq cm (b) 80 sq cm (c) 320 sq cm (d) 100 sq cm
28. 28.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 97 sq cm (d) 64 sq cm
29. 29.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) 4 times (c) 8 times (d) 5 times
30. 30.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 144 cu cm (d) 216 cu cm
31. 31.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
32. 32.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
33. 33.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 62 sq cm (b) 124 sq cm (c) 72 sq cm (d) 248 sq cm
34. 34.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 216 sq cm (d) 144 sq cm
35. 35.A cuboid is 10 cm long, 9 cm wide and 10 cm high. What is its total surface area? (a) 280 sq cm (b) 900 sq cm (c) 1120 sq cm (d) 560 sq cm
36. 36.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
37. 37.A cuboid is 11 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 44 cu cm (b) 24 cu cm (c) 396 cu cm (d) 358 cu cm
38. 38.A cuboid is 12 cm long, 10 cm wide and 7 cm high. What is its total surface area? (a) 548 sq cm (b) 274 sq cm (c) 1096 sq cm (d) 840 sq cm
39. 39.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 150 sq cm (c) 25 sq cm (d) 100 sq cm
40. 40.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 512 sq cm (d) 256 sq cm

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