Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 327 · 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 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
2. 2.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
3. 3.A cuboid is 6 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 72 sq cm (b) 216 sq cm (c) 108 sq cm (d) 54 sq cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
5. 5.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
6. 6.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
7. 7.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 144 sq cm (b) 73 sq cm (c) 36 sq cm (d) 72 sq cm
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
9. 9.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) 5 times (c) 25 times (d) 125 times
10. 10.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 486 sq cm (d) 81 sq cm
11. 11.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) 16 times (c) 4 times (d) 64 times
12. 12.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
15. 15.A cuboid is 7 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 21 cu cm (b) 315 cu cm (c) 286 cu cm (d) 35 cu cm
16. 16.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
18. 18.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
19. 19.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
20. 20.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
23. 23.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 72 cu cm (c) 13 cu cm (d) 108 cu cm
24. 24.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
25. 25.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 49 sq cm (d) 294 sq cm
26. 26.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
27. 27.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
28. 28.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
29. 29.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
31. 31.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) 8 times (c) 6 times (d) 2 times
32. 32.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 20 sq cm (b) 16 sq cm (c) 80 sq cm (d) 40 sq cm
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
34. 34.A cuboid is 7 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 15 cu cm (b) 105 cu cm (c) 21 cu cm (d) 142 cu cm
35. 35.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
36. 36.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
37. 37.A cuboid is 11 cm long, 8 cm wide and 9 cm high. What is its volume? (a) 792 cu cm (b) 28 cu cm (c) 88 cu cm (d) 518 cu cm
38. 38.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
39. 39.A cuboid is 11 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 96 cu cm (b) 15 cu cm (c) 22 cu cm (d) 44 cu cm
40. 40.A cuboid is 9 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 62 sq cm (b) 124 sq cm (c) 248 sq cm (d) 72 sq cm

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