Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 536 · 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 radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
2. 2.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
3. 3.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 6 cu cm (d) 24 cu cm
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
7. 7.A cuboid is 10 cm long, 9 cm wide and 3 cm high. What is its volume? (a) 294 cu cm (b) 90 cu cm (c) 22 cu cm (d) 270 cu cm
8. 8.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 294 sq cm (c) 343 sq cm (d) 196 sq cm
9. 9.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 2 times (d) 4 times
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
14. 14.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
15. 15.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
16. 16.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 144 cu cm (c) 217 cu cm (d) 18 cu cm
17. 17.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 54 cu cm (d) 9 cu cm
18. 18.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) 16 times (d) 8 times
19. 19.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
20. 20.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) 5 times (c) 10 times (d) 125 times
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
22. 22.A cuboid is 10 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 432 sq cm (b) 180 sq cm (c) 108 sq cm (d) 216 sq cm
23. 23.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
24. 24.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
26. 26.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
27. 27.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
28. 28.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
31. 31.A cuboid is 8 cm long, 7 cm wide and 10 cm high. What is its total surface area? (a) 206 sq cm (b) 824 sq cm (c) 412 sq cm (d) 560 sq cm
32. 32.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 125 sq cm (d) 100 sq cm
33. 33.A cuboid is 11 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 33 cu cm (b) 122 cu cm (c) 16 cu cm (d) 66 cu cm
34. 34.A cuboid is 12 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 180 cu cm (b) 222 cu cm (c) 60 cu cm (d) 20 cu cm
35. 35.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
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
37. 37.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 144 sq cm (d) 216 sq cm
38. 38.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 24 sq cm (c) 4 sq cm (d) 16 sq cm
39. 39.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 52 cu cm (b) 9 cu cm (c) 24 cu cm (d) 8 cu cm
40. 40.A cuboid is 6 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 108 cu cm (b) 72 cu cm (c) 18 cu cm (d) 13 cu cm

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