Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 202 · 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 circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
2. 2.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) 4 times (c) 2 times (d) 5 times
3. 3.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
4. 4.A cuboid is 7 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 190 sq cm (b) 380 sq cm (c) 95 sq cm (d) 175 sq cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 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) 2 times (b) 4 times (c) 8 times (d) 5 times
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
9. 9.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
11. 11.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
12. 12.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
13. 13.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
14. 14.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
15. 15.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
16. 16.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 144 sq cm (c) 217 sq cm (d) 216 sq cm
17. 17.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
18. 18.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) 64 times (c) 8 times (d) 16 times
19. 19.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 36 sq cm (d) 27 sq cm
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
21. 21.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
23. 23.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 30 cu cm
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
25. 25.A cuboid is 9 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 108 sq cm (b) 300 sq cm (c) 150 sq cm (d) 75 sq cm
26. 26.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 729 cu cm (c) 27 cu cm (d) 324 cu cm
27. 27.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
28. 28.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 36 cu cm (c) 9 cu cm (d) 27 cu cm
29. 29.A cuboid is 12 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 372 sq cm (b) 744 sq cm (c) 360 sq cm (d) 186 sq cm
30. 30.A cuboid is 12 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 25 cu cm (b) 108 cu cm (c) 432 cu cm (d) 384 cu cm
31. 31.A cuboid is 6 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 72 sq cm (b) 216 sq cm (c) 54 sq cm (d) 108 sq cm
32. 32.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) 5 times (c) 2 times (d) 8 times
33. 33.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 576 cu cm (d) 36 cu cm
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
35. 35.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
36. 36.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) 3 times (c) 6 times (d) 9 times
37. 37.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 87 sq cm (b) 348 sq cm (c) 174 sq cm (d) 135 sq cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 48 sq cm (b) 24 sq cm (c) 96 sq cm (d) 20 sq cm
39. 39.A cuboid is 10 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 536 sq cm (b) 240 sq cm (c) 268 sq cm (d) 134 sq cm
40. 40.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm

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