Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 542 · 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 radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
2. 2.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
4. 4.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
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
6. 6.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
7. 7.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
9. 9.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
10. 10.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) 5 times (c) 125 times (d) 10 times
11. 11.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 24 cu cm (d) 16 cu cm
12. 12.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 96 cu cm (c) 12 cu cm (d) 65 cu cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
15. 15.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) 10 times (d) 5 times
16. 16.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
17. 17.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 100 cu cm (c) 15 cu cm (d) 150 cu cm
18. 18.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
19. 19.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
20. 20.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
21. 21.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
22. 22.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
23. 23.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 64 sq cm (b) 128 sq cm (c) 65 sq cm (d) 32 sq cm
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
25. 25.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) 16 times (c) 4 times (d) 8 times
26. 26.A cuboid is 10 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 188 sq cm (b) 752 sq cm (c) 376 sq cm (d) 480 sq cm
27. 27.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
29. 29.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
30. 30.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
31. 31.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 512 cu cm (d) 256 cu cm
32. 32.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) 5 times (c) 10 times (d) 25 times
33. 33.A cuboid is 12 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 360 sq cm (b) 372 sq cm (c) 744 sq cm (d) 186 sq cm
34. 34.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 486 sq cm (d) 324 sq cm
35. 35.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
36. 36.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
37. 37.A cuboid is 9 cm long, 8 cm wide and 4 cm high. What is its total surface area? (a) 560 sq cm (b) 288 sq cm (c) 280 sq cm (d) 140 sq cm
38. 38.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 190 cu cm (b) 126 cu cm (c) 18 cu cm (d) 127 cu cm
39. 39.A cuboid is 9 cm long, 7 cm wide and 5 cm high. What is its total surface area? (a) 315 sq cm (b) 286 sq cm (c) 572 sq cm (d) 143 sq cm
40. 40.A cuboid is 11 cm long, 9 cm wide and 8 cm high. What is its total surface area? (a) 1036 sq cm (b) 518 sq cm (c) 259 sq cm (d) 792 sq cm

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