Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 575 · 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 side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
4. 4.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 248 sq cm (b) 72 sq cm (c) 124 sq cm (d) 62 sq cm
5. 5.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) 125 times (d) 5 times
6. 6.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) 5 times (c) 25 times (d) 125 times
7. 7.A cuboid is 11 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 234 cu cm (b) 198 cu cm (c) 20 cu cm (d) 66 cu cm
8. 8.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 36 sq cm (c) 27 sq cm (d) 54 sq cm
9. 9.A cuboid is 10 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 164 sq cm (b) 120 sq cm (c) 328 sq cm (d) 82 sq cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
12. 12.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
13. 13.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
14. 14.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
15. 15.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
16. 16.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
17. 17.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
18. 18.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) 8 times (d) 64 times
19. 19.A cuboid is 11 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 580 sq cm (b) 264 sq cm (c) 145 sq cm (d) 290 sq cm
20. 20.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
21. 21.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 7 cu cm (b) 6 cu cm (c) 32 cu cm (d) 12 cu cm
22. 22.A cuboid is 9 cm long, 8 cm wide and 5 cm high. What is its volume? (a) 22 cu cm (b) 314 cu cm (c) 360 cu cm (d) 72 cu cm
23. 23.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
25. 25.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) 3 times (c) 27 times (d) 9 times
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
27. 27.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 30 cu cm (d) 1000 cu cm
28. 28.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
29. 29.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
30. 30.A cuboid is 11 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 55 cu cm (b) 550 cu cm (c) 26 cu cm (d) 430 cu cm
31. 31.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 576 cu cm (d) 36 cu cm
32. 32.A cuboid is 8 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 152 cu cm (b) 96 cu cm (c) 16 cu cm (d) 48 cu cm
33. 33.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 68 sq cm (b) 136 sq cm (c) 80 sq cm (d) 272 sq cm
34. 34.A cuboid is 9 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 54 cu cm (b) 25 cu cm (c) 540 cu cm (d) 408 cu cm
35. 35.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
36. 36.A cuboid is 5 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 92 sq cm (b) 184 sq cm (c) 160 sq cm (d) 368 sq cm
37. 37.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
38. 38.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 21 cu cm (d) 196 cu cm
39. 39.A cuboid is 11 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 200 cu cm (b) 19 cu cm (c) 132 cu cm (d) 66 cu cm
40. 40.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 16 cu cm (d) 24 cu cm

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