Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 476 · 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.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
2. 2.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) 64 times (d) 16 times
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
4. 4.If the side of a square 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
5. 5.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 196 sq cm (d) 294 sq cm
6. 6.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
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) 5 times (b) 8 times (c) 2 times (d) 4 times
8. 8.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) 10 times (d) 25 times
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
11. 11.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
12. 12.A cuboid is 7 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 210 sq cm (b) 214 sq cm (c) 428 sq cm (d) 107 sq cm
13. 13.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
14. 14.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) 4 times (c) 8 times (d) 6 times
15. 15.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
16. 16.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
17. 17.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 220 sq cm (b) 110 sq cm (c) 75 sq cm (d) 55 sq cm
18. 18.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
19. 19.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
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
21. 21.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 576 cu cm (c) 864 cu cm (d) 1728 cu cm
22. 22.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
23. 23.A cuboid is 7 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 15 cu cm (b) 42 cu cm (c) 84 cu cm (d) 136 cu cm
24. 24.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 484 cu cm (d) 726 cu cm
25. 25.A cuboid is 12 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 744 sq cm (b) 372 sq cm (c) 360 sq cm (d) 186 sq cm
26. 26.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
27. 27.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 100 sq cm (d) 600 sq cm
28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
29. 29.A cuboid is 10 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 18 cu cm (b) 160 cu cm (c) 40 cu cm (d) 192 cu cm
30. 30.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
31. 31.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 8 cu cm (b) 11 cu cm (c) 40 cu cm (d) 76 cu cm
32. 32.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
33. 33.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
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
35. 35.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) 125 times (c) 10 times (d) 5 times
36. 36.A cuboid is 7 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 147 sq cm (b) 364 sq cm (c) 182 sq cm (d) 91 sq cm
37. 37.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 32 cu cm (b) 7 cu cm (c) 6 cu cm (d) 12 cu cm
38. 38.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
39. 39.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 54 sq cm (d) 9 sq cm
40. 40.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 144 sq cm (c) 36 sq cm (d) 216 sq cm

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