Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 561 · 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 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
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
3. 3.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
7. 7.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
8. 8.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 16 sq cm (d) 64 sq cm
9. 9.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
10. 10.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
11. 11.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 80 cu cm (b) 15 cu cm (c) 10 cu cm (d) 132 cu cm
12. 12.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 16 cu cm (d) 6 cu cm
13. 13.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
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
16. 16.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 216 sq cm (d) 217 sq cm
17. 17.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) 125 times (d) 10 times
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
19. 19.If the side of a square 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
20. 20.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
21. 21.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
22. 22.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
23. 23.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 400 cu cm (d) 1000 cu cm
24. 24.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) 5 times (c) 4 times (d) 8 times
25. 25.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
26. 26.A cuboid is 5 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 142 cu cm (b) 105 cu cm (c) 15 cu cm (d) 106 cu cm
27. 27.A cuboid is 7 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 286 sq cm (b) 572 sq cm (c) 143 sq cm (d) 315 sq cm
28. 28.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) 2 times (d) 5 times
29. 29.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 216 cu cm (d) 144 cu cm
30. 30.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 220 cu cm (b) 200 cu cm (c) 20 cu cm (d) 19 cu cm
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
32. 32.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
33. 33.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
34. 34.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 17 cu cm (b) 164 cu cm (c) 12 cu cm (d) 120 cu cm
35. 35.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
36. 36.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 196 cu cm (d) 21 cu cm
37. 37.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
38. 38.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
39. 39.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
40. 40.A cuboid is 10 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 26 cu cm (b) 440 cu cm (c) 60 cu cm (d) 600 cu cm

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