Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 107 · 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) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
2. 2.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
3. 3.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 8 sq cm (c) 4 sq cm (d) 16 sq cm
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
5. 5.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
6. 6.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 25 sq cm (c) 150 sq cm (d) 100 sq cm
7. 7.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 64 cu cm (d) 12 cu cm
8. 8.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
9. 9.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
10. 10.A cuboid is 6 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 416 sq cm (b) 104 sq cm (c) 192 sq cm (d) 208 sq cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
14. 14.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
15. 15.A cuboid is 8 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 202 cu cm (b) 168 cu cm (c) 24 cu cm (d) 18 cu cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
17. 17.A cuboid is 12 cm long, 10 cm wide and 4 cm high. What is its total surface area? (a) 480 sq cm (b) 208 sq cm (c) 832 sq cm (d) 416 sq cm
18. 18.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
19. 19.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) 8 times (d) 16 times
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
22. 22.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 64 sq cm (c) 16 sq cm (d) 96 sq cm
23. 23.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
26. 26.A cuboid is 9 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 300 sq cm (b) 150 sq cm (c) 108 sq cm (d) 75 sq cm
27. 27.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 36 cu cm (d) 27 cu cm
28. 28.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) 125 times (c) 10 times (d) 5 times
29. 29.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 24 cu cm (b) 52 cu cm (c) 12 cu cm (d) 9 cu cm
30. 30.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
31. 31.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) 4 times (d) 2 times
32. 32.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
33. 33.A cuboid is 5 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 284 sq cm (b) 142 sq cm (c) 105 sq cm (d) 71 sq cm
34. 34.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 40 sq cm (b) 20 sq cm (c) 80 sq cm (d) 16 sq cm
35. 35.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 576 cu cm
36. 36.A cuboid is 9 cm long, 7 cm wide and 10 cm high. What is its total surface area? (a) 223 sq cm (b) 892 sq cm (c) 446 sq cm (d) 630 sq cm
37. 37.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
38. 38.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
39. 39.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 75 sq cm (b) 55 sq cm (c) 110 sq cm (d) 220 sq cm
40. 40.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 42 cu cm (b) 17 cu cm (c) 188 cu cm (d) 168 cu cm

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