Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 489 · 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 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) 27 times (d) 3 times
2. 2.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 40 sq cm (b) 76 sq cm (c) 38 sq cm (d) 152 sq cm
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
6. 6.A cuboid is 11 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 504 sq cm (b) 252 sq cm (c) 176 sq cm (d) 126 sq cm
7. 7.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 264 sq cm (b) 66 sq cm (c) 132 sq cm (d) 80 sq 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) 125 times (b) 10 times (c) 25 times (d) 5 times
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
11. 11.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 1000 sq cm (c) 400 sq cm (d) 600 sq cm
12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
13. 13.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
14. 14.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
16. 16.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
17. 17.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
18. 18.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
19. 19.A cuboid is 11 cm long, 10 cm wide and 5 cm high. What is its volume? (a) 26 cu cm (b) 430 cu cm (c) 110 cu cm (d) 550 cu cm
20. 20.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 36 cu cm (c) 864 cu cm (d) 576 cu cm
21. 21.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
22. 22.A cuboid is 7 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 70 sq cm (b) 236 sq cm (c) 59 sq cm (d) 118 sq cm
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
24. 24.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 19 cu cm (b) 18 cu cm (c) 216 cu cm (d) 180 cu cm
25. 25.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 54 sq cm (d) 9 sq cm
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
27. 27.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
28. 28.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 36 sq cm (b) 72 sq cm (c) 73 sq cm (d) 144 sq cm
29. 29.A cuboid is 12 cm long, 8 cm wide and 7 cm high. What is its volume? (a) 96 cu cm (b) 27 cu cm (c) 472 cu cm (d) 672 cu cm
30. 30.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
31. 31.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
32. 32.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
33. 33.A cuboid is 9 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 18 cu cm (b) 256 cu cm (c) 21 cu cm (d) 180 cu cm
34. 34.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
35. 35.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 24 cu cm (b) 48 cu cm (c) 12 cu cm (d) 88 cu cm
36. 36.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) 10 times (c) 5 times (d) 125 times
37. 37.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
38. 38.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) 16 times (c) 8 times (d) 64 times
39. 39.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 125 cu cm (d) 100 cu cm
40. 40.A cuboid is 10 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 19 cu cm (b) 216 cu cm (c) 30 cu cm (d) 180 cu cm

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