Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 404 · 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 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 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) 27 times (c) 6 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.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) 10 times (d) 5 times
5. 5.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
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
7. 7.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) 64 times (c) 4 times (d) 8 times
8. 8.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
9. 9.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 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) 125 times (c) 10 times (d) 25 times
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
13. 13.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 384 cu cm (d) 512 cu cm
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
15. 15.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 343 cu cm (d) 196 cu cm
16. 16.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) 9 times (c) 3 times (d) 6 times
17. 17.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
18. 18.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 217 sq cm (c) 216 sq cm (d) 36 sq cm
19. 19.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
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
21. 21.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
22. 22.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 27 cu cm (d) 54 cu cm
23. 23.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 12 cu cm (d) 96 cu cm
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
25. 25.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 726 sq cm (c) 484 sq cm (d) 1331 sq cm
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
27. 27.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 11 cu cm (b) 8 cu cm (c) 76 cu cm (d) 40 cu cm
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
29. 29.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
30. 30.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 486 sq cm (d) 324 sq cm
31. 31.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 82 sq cm (b) 41 sq cm (c) 164 sq cm (d) 42 sq cm
32. 32.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
33. 33.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 6 cu cm (b) 32 cu cm (c) 7 cu cm (d) 12 cu cm
34. 34.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 64 sq cm (b) 32 sq cm (c) 16 sq cm (d) 12 sq cm
35. 35.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
36. 36.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
37. 37.A cuboid is 10 cm long, 7 cm wide and 5 cm high. What is its volume? (a) 70 cu cm (b) 310 cu cm (c) 350 cu cm (d) 22 cu cm
38. 38.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
39. 39.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
40. 40.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times

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