Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 334 · 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.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) 2 times (d) 4 times
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
3. 3.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
4. 4.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
5. 5.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
6. 6.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
7. 7.A cuboid is 9 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 174 sq cm (b) 348 sq cm (c) 87 sq cm (d) 135 sq cm
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
11. 11.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
12. 12.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
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
14. 14.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 111 sq cm (b) 444 sq cm (c) 222 sq cm (d) 189 sq cm
15. 15.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 729 sq cm (c) 324 sq cm (d) 81 sq cm
16. 16.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 8 cu cm (d) 6 cu cm
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
18. 18.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
19. 19.A cuboid is 8 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 320 sq cm (b) 160 sq cm (c) 384 sq cm (d) 640 sq cm
20. 20.A cuboid is 10 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 164 sq cm (b) 120 sq cm (c) 82 sq cm (d) 328 sq cm
21. 21.A cuboid is 10 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 210 cu cm (b) 30 cu cm (c) 20 cu cm (d) 242 cu cm
22. 22.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 80 sq cm (c) 20 sq cm (d) 40 sq cm
23. 23.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
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) 3 times (c) 6 times (d) 9 times
25. 25.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 384 cu cm (d) 24 cu cm
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
27. 27.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 8 sq cm (c) 16 sq cm (d) 24 sq cm
28. 28.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) 125 times (c) 25 times (d) 10 times
29. 29.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 27 sq cm (d) 9 sq cm
30. 30.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
31. 31.A cuboid is 8 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 192 cu cm (b) 16 cu cm (c) 128 cu cm (d) 18 cu cm
32. 32.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
33. 33.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) 8 times (c) 64 times (d) 16 times
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
37. 37.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 80 cu cm (b) 8 cu cm (c) 16 cu cm (d) 136 cu cm
38. 38.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
39. 39.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
40. 40.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 400 cu cm

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