Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 690 · 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) 125 times (b) 5 times (c) 25 times (d) 10 times
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
3. 3.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 294 cu cm (d) 21 cu cm
4. 4.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
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
6. 6.A cuboid is 7 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 294 sq cm (b) 266 sq cm (c) 532 sq cm (d) 133 sq cm
7. 7.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 168 cu cm (b) 188 cu cm (c) 24 cu cm (d) 17 cu cm
8. 8.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
9. 9.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) 4 times (c) 64 times (d) 16 times
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
11. 11.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) 6 times (c) 8 times (d) 2 times
12. 12.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
13. 13.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) 64 times (d) 16 times
14. 14.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) 27 times (c) 6 times (d) 9 times
15. 15.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
16. 16.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
18. 18.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 102 sq cm (b) 51 sq cm (c) 204 sq cm (d) 54 sq cm
19. 19.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
20. 20.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
21. 21.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) 27 times (c) 6 times (d) 9 times
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
23. 23.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 256 cu cm (c) 24 cu cm (d) 384 cu cm
24. 24.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
25. 25.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
26. 26.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 16 sq cm (d) 97 sq cm
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
28. 28.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 512 sq cm (c) 256 sq cm (d) 64 sq cm
29. 29.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 144 cu cm (d) 216 cu cm
30. 30.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
31. 31.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
32. 32.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 150 sq cm (d) 125 sq cm
33. 33.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
34. 34.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
35. 35.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
36. 36.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
37. 37.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 27 cu cm (d) 486 cu cm
38. 38.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
39. 39.A cuboid is 12 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 104 cu cm (c) 24 cu cm (d) 16 cu cm
40. 40.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

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