Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 580 · 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) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
2. 2.A cuboid is 8 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 16 cu cm (b) 97 cu cm (c) 96 cu cm (d) 152 cu cm
3. 3.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 36 sq cm (d) 54 sq cm
4. 4.A cuboid is 10 cm long, 8 cm wide and 9 cm high. What is its volume? (a) 27 cu cm (b) 720 cu cm (c) 80 cu cm (d) 484 cu cm
5. 5.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
8. 8.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 90 sq cm (b) 292 sq cm (c) 146 sq cm (d) 73 sq cm
9. 9.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
10. 10.A cuboid is 12 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 222 cu cm (b) 180 cu cm (c) 20 cu cm (d) 60 cu cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
12. 12.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
14. 14.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) 125 times (c) 5 times (d) 10 times
15. 15.A cuboid is 5 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 260 sq cm (b) 100 sq cm (c) 65 sq cm (d) 130 sq cm
16. 16.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 cu cm
17. 17.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
18. 18.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
19. 19.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
21. 21.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) 5 times (d) 4 times
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
24. 24.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 102 cu cm (b) 14 cu cm (c) 6 cu cm (d) 54 cu cm
25. 25.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
26. 26.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
27. 27.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 17 cu cm (b) 180 cu cm (c) 18 cu cm (d) 144 cu cm
28. 28.A cuboid is 7 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 214 cu cm (b) 18 cu cm (c) 210 cu cm (d) 35 cu cm
29. 29.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) 8 times (c) 16 times (d) 4 times
30. 30.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 24 cu cm (d) 16 cu cm
31. 31.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 60 cu cm (b) 30 cu cm (c) 13 cu cm (d) 104 cu cm
32. 32.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 36 cu cm (d) 27 cu cm
33. 33.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 4 sq cm (c) 8 sq cm (d) 16 sq cm
34. 34.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
36. 36.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 100 sq cm (c) 150 sq cm (d) 25 sq cm
37. 37.A cuboid is 11 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 206 sq cm (b) 412 sq cm (c) 165 sq cm (d) 103 sq cm
38. 38.A cuboid is 10 cm long, 7 cm wide and 3 cm high. What is its total surface area? (a) 121 sq cm (b) 210 sq cm (c) 484 sq cm (d) 242 sq cm
39. 39.A cuboid is 5 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 404 sq cm (b) 101 sq cm (c) 180 sq cm (d) 202 sq cm
40. 40.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times

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