Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 924 · 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.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 36 sq cm (d) 217 sq cm
2. 2.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
3. 3.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
4. 4.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
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
6. 6.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 126 cu cm (b) 14 cu cm (c) 15 cu cm (d) 90 cu cm
7. 7.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) 4 times (c) 5 times (d) 2 times
8. 8.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 190 sq cm (b) 150 sq cm (c) 380 sq cm (d) 95 sq cm
9. 9.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
10. 10.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 486 sq cm (c) 729 sq cm (d) 81 sq cm
11. 11.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 125 cu cm (d) 100 cu cm
12. 12.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
13. 13.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 cu cm
14. 14.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 217 cu cm (c) 18 cu cm (d) 216 cu cm
15. 15.A cuboid is 11 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 231 sq cm (b) 131 sq cm (c) 262 sq cm (d) 524 sq cm
16. 16.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
17. 17.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
19. 19.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
20. 20.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
22. 22.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) 3 times (c) 6 times (d) 9 times
23. 23.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) 10 times (c) 125 times (d) 5 times
24. 24.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
25. 25.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
26. 26.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
27. 27.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
28. 28.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
29. 29.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 8 times (d) 4 times
31. 31.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) 3 times (c) 27 times (d) 9 times
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
33. 33.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
34. 34.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 64 cu cm (d) 65 cu cm
35. 35.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
36. 36.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) 10 times (c) 5 times (d) 125 times
37. 37.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
38. 38.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 729 cu cm (d) 324 cu cm
39. 39.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
40. 40.A cuboid is 12 cm long, 10 cm wide and 6 cm high. What is its total surface area? (a) 252 sq cm (b) 720 sq cm (c) 504 sq cm (d) 1008 sq cm

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