Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 973 · 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 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
2. 2.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
3. 3.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
4. 4.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
5. 5.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
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
7. 7.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
8. 8.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
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 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) 125 times (b) 25 times (c) 5 times (d) 10 times
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
12. 12.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 144 sq cm (c) 576 sq cm (d) 864 sq cm
13. 13.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
14. 14.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
15. 15.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 26 sq cm (b) 104 sq cm (c) 52 sq cm (d) 24 sq cm
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
17. 17.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
18. 18.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 400 cu cm (d) 30 cu cm
19. 19.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
20. 20.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
21. 21.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 64 cu cm (d) 12 cu cm
22. 22.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
23. 23.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
24. 24.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) 16 times (d) 4 times
25. 25.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
26. 26.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
27. 27.A cuboid is 7 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 164 sq cm (b) 42 sq cm (c) 82 sq cm (d) 41 sq cm
28. 28.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 18 cu cm (b) 126 cu cm (c) 127 cu cm (d) 190 cu cm
29. 29.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 64 sq cm (c) 384 sq cm (d) 512 sq cm
30. 30.A cuboid is 11 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 412 sq cm (b) 206 sq cm (c) 165 sq cm (d) 103 sq cm
31. 31.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) 3 times (d) 6 times
32. 32.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
33. 33.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
34. 34.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 217 cu cm (c) 18 cu cm (d) 144 cu cm
35. 35.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
36. 36.A cuboid is 10 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 121 sq cm (b) 242 sq cm (c) 210 sq cm (d) 484 sq cm
37. 37.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 204 sq cm (b) 54 sq cm (c) 102 sq cm (d) 51 sq cm
38. 38.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 125 cu cm (d) 15 cu cm
39. 39.A cuboid is 12 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 156 sq cm (b) 624 sq cm (c) 288 sq cm (d) 312 sq cm
40. 40.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm

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