Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 115 · 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 radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
2. 2.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) 9 times (c) 27 times (d) 3 times
3. 3.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
4. 4.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 60 sq cm (b) 224 sq cm (c) 56 sq cm (d) 112 sq cm
5. 5.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
6. 6.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 96 sq cm (d) 97 sq cm
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
10. 10.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 144 sq cm
11. 11.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 222 cu cm (b) 27 cu cm (c) 189 cu cm (d) 19 cu cm
12. 12.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
14. 14.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
15. 15.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 1331 sq cm (c) 726 sq cm (d) 121 sq cm
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
17. 17.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
18. 18.A cuboid is 9 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 174 sq cm (b) 135 sq cm (c) 348 sq cm (d) 87 sq cm
19. 19.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
20. 20.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
21. 21.A cuboid is 8 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 152 cu cm (b) 96 cu cm (c) 97 cu cm (d) 16 cu cm
22. 22.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) 10 times (c) 25 times (d) 125 times
23. 23.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) 8 times (c) 2 times (d) 4 times
24. 24.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 13 cu cm (b) 60 cu cm (c) 104 cu cm (d) 30 cu cm
25. 25.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 73 sq cm (b) 144 sq cm (c) 72 sq cm (d) 36 sq cm
26. 26.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
27. 27.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 256 cu cm (d) 384 cu 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) 64 times (b) 16 times (c) 8 times (d) 4 times
29. 29.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 96 cu cm (b) 152 cu cm (c) 16 cu cm (d) 12 cu cm
30. 30.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
31. 31.A cuboid is 12 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 216 sq cm (b) 576 sq cm (c) 432 sq cm (d) 864 sq cm
32. 32.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
33. 33.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
34. 34.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 576 cu cm (d) 1728 cu cm
35. 35.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 144 cu cm (d) 18 cu cm
36. 36.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
37. 37.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) 125 times (c) 5 times (d) 25 times
38. 38.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
39. 39.A cuboid is 10 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 50 cu cm (b) 18 cu cm (c) 190 cu cm (d) 150 cu cm
40. 40.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 7 cu cm (b) 6 cu cm (c) 12 cu cm (d) 32 cu cm

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