Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 654 · 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 3 cm. What is its total surface area? (a) 36 sq cm (b) 9 sq cm (c) 27 sq cm (d) 54 sq cm
2. 2.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 144 cu cm (c) 217 cu cm (d) 18 cu cm
3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
4. 4.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
6. 6.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 343 cu cm (d) 21 cu cm
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
8. 8.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) 9 times (c) 6 times (d) 27 times
9. 9.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) 5 times (c) 10 times (d) 125 times
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
11. 11.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
12. 12.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
13. 13.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
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
16. 16.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
17. 17.A cuboid is 7 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 144 cu cm (b) 28 cu cm (c) 15 cu cm (d) 112 cu cm
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
19. 19.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
20. 20.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 8 sq cm (d) 24 sq 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) 6 times (c) 27 times (d) 9 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) 5 times (b) 25 times (c) 10 times (d) 125 times
23. 23.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 484 sq cm (c) 726 sq cm (d) 121 sq cm
24. 24.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
25. 25.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
26. 26.A cuboid is 11 cm long, 7 cm wide and 7 cm high. What is its volume? (a) 77 cu cm (b) 25 cu cm (c) 539 cu cm (d) 406 cu cm
27. 27.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
28. 28.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 512 cu cm (d) 24 cu cm
29. 29.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
30. 30.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
31. 31.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 343 sq cm (c) 49 sq cm (d) 196 sq cm
32. 32.A cuboid is 6 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 112 sq cm (b) 28 sq cm (c) 24 sq cm (d) 56 sq cm
33. 33.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 384 sq cm (d) 64 sq cm
34. 34.A cuboid is 11 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 264 sq cm (b) 145 sq cm (c) 580 sq cm (d) 290 sq cm
35. 35.A cuboid is 12 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 216 sq cm (c) 300 sq cm (d) 600 sq cm
36. 36.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 15 cu cm (d) 125 cu cm
37. 37.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) 10 times (c) 125 times (d) 25 times
38. 38.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
39. 39.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
40. 40.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm

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