Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 565 · 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 area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
4. 4.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
5. 5.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
6. 6.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
8. 8.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
10. 10.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
11. 11.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 384 sq cm (d) 512 sq cm
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
13. 13.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 49 sq cm (d) 294 sq cm
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
15. 15.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 40 sq cm (b) 38 sq cm (c) 76 sq cm (d) 152 sq cm
16. 16.A cuboid is 10 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 50 cu cm (b) 400 cu cm (c) 25 cu cm (d) 500 cu cm
17. 17.A cuboid is 12 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 192 cu cm (b) 19 cu cm (c) 144 cu cm (d) 36 cu cm
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
19. 19.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 217 cu cm (d) 216 cu cm
20. 20.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 16 cu cm (d) 8 cu cm
21. 21.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 600 sq cm (c) 400 sq cm (d) 100 sq cm
22. 22.A cuboid is 9 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 102 sq cm (b) 51 sq cm (c) 54 sq cm (d) 204 sq cm
23. 23.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 27 cu cm (d) 36 cu cm
24. 24.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 1331 sq cm (c) 121 sq cm (d) 726 sq cm
25. 25.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 9 sq cm (d) 54 sq cm
26. 26.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
27. 27.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
28. 28.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 6 times (d) 8 times
29. 29.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
30. 30.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
31. 31.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
32. 32.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
33. 33.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
34. 34.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
35. 35.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 104 sq cm (b) 52 sq cm (c) 24 sq cm (d) 26 sq cm
36. 36.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 1000 cu cm (c) 600 cu cm (d) 400 cu cm
37. 37.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) 3 times (c) 9 times (d) 27 times
38. 38.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 112 cu cm (b) 15 cu cm (c) 6 cu cm (d) 60 cu cm
39. 39.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
40. 40.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times

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