Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 549 · 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 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 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) 10 times (b) 5 times (c) 125 times (d) 25 times
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
4. 4.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) 8 times (c) 5 times (d) 4 times
5. 5.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 256 cu cm (d) 384 cu cm
6. 6.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
7. 7.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
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
11. 11.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
12. 12.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 112 cu cm (b) 14 cu cm (c) 8 cu cm (d) 64 cu cm
13. 13.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
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
15. 15.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
16. 16.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 12 cu cm (b) 11 cu cm (c) 48 cu cm (d) 80 cu cm
17. 17.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
18. 18.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 864 cu cm
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
20. 20.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 486 sq cm (c) 324 sq cm (d) 81 sq cm
21. 21.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) 27 times (c) 6 times (d) 3 times
22. 22.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) 16 times (c) 4 times (d) 64 times
23. 23.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
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
25. 25.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
26. 26.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
27. 27.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 64 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) 5 times (b) 125 times (c) 25 times (d) 10 times
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
30. 30.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
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
32. 32.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 100 sq cm (c) 600 sq cm (d) 400 sq cm
33. 33.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 102 cu cm (b) 54 cu cm (c) 6 cu cm (d) 14 cu cm
34. 34.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 125 cu cm (c) 150 cu cm (d) 15 cu cm
35. 35.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
36. 36.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
37. 37.A cuboid is 10 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 304 cu cm (b) 22 cu cm (c) 40 cu cm (d) 320 cu cm
38. 38.A cuboid is 7 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 70 cu cm (c) 118 cu cm (d) 35 cu cm
39. 39.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 144 sq cm (d) 216 sq cm
40. 40.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 18 cu cm (b) 21 cu cm (c) 168 cu cm (d) 202 cu cm

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