Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 552 · 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 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
2. 2.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm
3. 3.If the radius of a circle 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
4. 4.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
5. 5.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) 16 times (c) 4 times (d) 8 times
6. 6.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
7. 7.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 9 cu cm (d) 54 cu cm
8. 8.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) 125 times (c) 25 times (d) 10 times
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
10. 10.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
12. 12.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
13. 13.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
14. 14.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
15. 15.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
17. 17.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 144 sq cm (c) 864 sq cm (d) 1728 sq cm
18. 18.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 196 cu cm (d) 21 cu cm
19. 19.A cuboid is 12 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 600 sq cm (c) 300 sq cm (d) 216 sq cm
20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
21. 21.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) 5 times (c) 4 times (d) 8 times
22. 22.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 294 sq cm (d) 49 sq cm
23. 23.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 2 times (d) 6 times
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
25. 25.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 10 cu cm (b) 36 cu cm (c) 66 cu cm (d) 12 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) 5 times (c) 4 times (d) 2 times
27. 27.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
28. 28.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
29. 29.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 384 sq cm (d) 512 sq cm
30. 30.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
31. 31.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) 8 times (c) 16 times (d) 64 times
32. 32.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 6 cu cm (b) 36 cu cm (c) 11 cu cm (d) 72 cu cm
33. 33.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 380 sq cm (b) 95 sq cm (c) 190 sq cm (d) 126 sq cm
34. 34.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 400 cu cm (d) 1000 cu cm
35. 35.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
36. 36.A cuboid is 8 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 40 cu cm (b) 184 cu cm (c) 17 cu cm (d) 160 cu cm
37. 37.A cuboid is 6 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 144 sq cm (b) 84 sq cm (c) 168 sq cm (d) 336 sq cm
38. 38.A cuboid is 12 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 162 sq cm (b) 324 sq cm (c) 360 sq cm (d) 648 sq cm
39. 39.A cuboid is 9 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 126 cu cm (b) 81 cu cm (c) 27 cu cm (d) 15 cu cm
40. 40.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm

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