Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 188 · 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 circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
3. 3.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 2 times (d) 6 times
6. 6.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
7. 7.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 54 sq cm (b) 216 sq cm (c) 72 sq cm (d) 108 sq cm
8. 8.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 84 sq cm (b) 42 sq cm (c) 18 sq cm (d) 21 sq cm
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
10. 10.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 1728 sq cm (d) 144 sq cm
11. 11.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 36 cu cm (d) 54 cu cm
12. 12.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) 4 times (c) 8 times (d) 2 times
13. 13.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
14. 14.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
15. 15.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 120 sq cm (b) 296 sq cm (c) 148 sq cm (d) 74 sq cm
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
17. 17.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 726 sq cm (d) 484 sq cm
18. 18.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
19. 19.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) 6 times (c) 3 times (d) 9 times
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
22. 22.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
23. 23.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
24. 24.A cuboid is 9 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 62 sq cm (b) 124 sq cm (c) 248 sq cm (d) 72 sq cm
25. 25.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
26. 26.A cuboid is 10 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 256 cu cm (b) 180 cu cm (c) 21 cu cm (d) 20 cu 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) 4 times (b) 8 times (c) 64 times (d) 16 times
28. 28.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 150 cu cm (d) 100 cu cm
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
30. 30.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 400 sq cm
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
32. 32.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
33. 33.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
34. 34.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 126 cu cm (b) 127 cu cm (c) 190 cu cm (d) 18 cu cm
35. 35.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
37. 37.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
38. 38.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 196 cu cm (d) 343 cu cm
39. 39.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 95 sq cm (b) 126 sq cm (c) 380 sq cm (d) 190 sq cm
40. 40.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 16 cu cm (d) 8 cu cm

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