Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 170 · 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) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
2. 2.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
4. 4.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) 4 times (c) 64 times (d) 8 times
5. 5.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
7. 7.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
8. 8.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 600 sq cm
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
10. 10.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
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
13. 13.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
14. 14.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) 8 times (c) 4 times (d) 2 times
15. 15.A cuboid is 9 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 22 cu cm (b) 27 cu cm (c) 270 cu cm (d) 294 cu cm
16. 16.A cuboid is 9 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 230 cu cm (b) 45 cu cm (c) 225 cu cm (d) 19 cu cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 46 sq cm (b) 92 sq cm (c) 48 sq cm (d) 184 sq cm
18. 18.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 10 cu cm (b) 8 cu cm (c) 32 cu cm (d) 64 cu cm
19. 19.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
20. 20.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) 5 times (c) 10 times (d) 125 times
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
22. 22.A cuboid is 12 cm long, 6 cm wide and 9 cm high. What is its volume? (a) 27 cu cm (b) 72 cu cm (c) 468 cu cm (d) 648 cu cm
23. 23.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
24. 24.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) 64 times (d) 16 times
25. 25.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 348 sq cm (b) 174 sq cm (c) 87 sq cm (d) 135 sq cm
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
27. 27.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 486 sq cm (d) 729 sq cm
28. 28.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 72 cu cm (c) 11 cu cm (d) 36 cu cm
29. 29.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) 25 times (c) 5 times (d) 10 times
30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
32. 32.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 217 cu cm (c) 18 cu cm (d) 216 cu cm
33. 33.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
34. 34.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
35. 35.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 72 sq cm (b) 36 sq cm (c) 73 sq cm (d) 144 sq cm
36. 36.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) 8 times (c) 2 times (d) 5 times
37. 37.A cuboid is 8 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 340 cu cm (b) 400 cu cm (c) 40 cu cm (d) 23 cu cm
38. 38.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 144 sq cm (d) 216 sq cm
39. 39.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
40. 40.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 24 sq cm (d) 8 sq cm

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