Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 463 · 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 area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
2. 2.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 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) 27 times (b) 3 times (c) 9 times (d) 6 times
4. 4.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
5. 5.A cuboid is 9 cm long, 8 cm wide and 5 cm high. What is its volume? (a) 360 cu cm (b) 314 cu cm (c) 22 cu cm (d) 72 cu cm
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 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.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
9. 9.A cuboid is 7 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 71 cu cm (b) 70 cu cm (c) 118 cu cm (d) 14 cu cm
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
11. 11.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
12. 12.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
13. 13.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
14. 14.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
15. 15.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
16. 16.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
17. 17.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
18. 18.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
19. 19.If the radius of a circle 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
20. 20.A cuboid is 11 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 442 cu cm (b) 77 cu cm (c) 616 cu cm (d) 26 cu cm
21. 21.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 96 cu cm (d) 64 cu cm
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
23. 23.A cuboid is 6 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 270 cu cm (b) 30 cu cm (c) 20 cu cm (d) 258 cu cm
24. 24.If the side of a square 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
25. 25.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
27. 27.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
28. 28.If the radius of a circle 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
29. 29.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 726 cu cm (c) 33 cu cm (d) 484 cu cm
30. 30.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
31. 31.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
32. 32.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 36 cu cm (c) 27 cu cm (d) 9 cu cm
33. 33.A cuboid is 10 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 160 cu cm (b) 161 cu cm (c) 20 cu cm (d) 232 cu cm
34. 34.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 60 cu cm (b) 13 cu cm (c) 30 cu cm (d) 104 cu cm
35. 35.A cuboid is 12 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 84 cu cm (b) 21 cu cm (c) 244 cu cm (d) 168 cu cm
36. 36.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 9 sq cm (c) 54 sq cm (d) 27 sq cm
37. 37.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) 9 times (c) 3 times (d) 27 times
38. 38.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
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 8 times (d) 4 times
40. 40.A cuboid is 10 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 60 cu cm (c) 112 cu cm (d) 20 cu cm

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