Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 242 · 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 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
2. 2.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 248 sq cm (b) 62 sq cm (c) 124 sq cm (d) 72 sq cm
3. 3.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 32 sq cm (c) 64 sq cm (d) 12 sq cm
4. 4.A cuboid is 9 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 124 cu cm (b) 72 cu cm (c) 15 cu cm (d) 18 cu cm
5. 5.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
7. 7.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 726 sq cm (c) 121 sq cm (d) 484 sq cm
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
9. 9.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) 8 times (d) 4 times
10. 10.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) 64 times (d) 8 times
11. 11.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 16 sq cm (d) 97 sq cm
12. 12.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
17. 17.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 486 cu cm (c) 324 cu cm (d) 27 cu 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) 10 times (b) 25 times (c) 5 times (d) 125 times
19. 19.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 47 sq cm (b) 188 sq cm (c) 94 sq cm (d) 60 sq cm
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
22. 22.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 8 cu cm (d) 16 cu cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 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) 3 times (c) 6 times (d) 9 times
25. 25.A cuboid is 7 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 140 cu cm (b) 35 cu cm (c) 166 cu cm (d) 16 cu cm
26. 26.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) 2 times (c) 4 times (d) 5 times
27. 27.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) 5 times (d) 25 times
28. 28.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
29. 29.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
30. 30.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
31. 31.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 44 sq cm (b) 88 sq cm (c) 176 sq cm (d) 48 sq cm
32. 32.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) 27 times (c) 6 times (d) 9 times
33. 33.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
34. 34.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 40 cu cm (d) 17 cu cm
35. 35.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 54 cu cm (d) 9 cu cm
36. 36.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
37. 37.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 146 sq cm (b) 292 sq cm (c) 90 sq cm (d) 73 sq cm
38. 38.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) 8 times (c) 16 times (d) 64 times
39. 39.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 20 cu cm (b) 27 cu cm (c) 216 cu cm (d) 246 cu cm
40. 40.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 125 cu cm (d) 150 cu cm

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