Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 307 · 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 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
6. 6.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
7. 7.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 82 sq cm (b) 328 sq cm (c) 120 sq cm (d) 164 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) 9 times (b) 6 times (c) 3 times (d) 27 times
9. 9.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
10. 10.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 96 cu cm (d) 64 cu cm
11. 11.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 8 times (c) 4 times (d) 2 times
12. 12.A cuboid is 10 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 332 cu cm (b) 40 cu cm (c) 23 cu cm (d) 360 cu cm
13. 13.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 216 cu cm (d) 217 cu cm
14. 14.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 24 sq cm (d) 8 sq cm
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
16. 16.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
17. 17.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
18. 18.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
20. 20.If the radius of a circle 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
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
22. 22.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
23. 23.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
25. 25.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
27. 27.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
28. 28.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
29. 29.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
30. 30.A cuboid is 12 cm long, 11 cm wide and 2 cm high. What is its total surface area? (a) 264 sq cm (b) 178 sq cm (c) 712 sq cm (d) 356 sq cm
31. 31.A cuboid is 7 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 71 cu cm (b) 14 cu cm (c) 118 cu cm (d) 70 cu cm
32. 32.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 36 sq cm (d) 27 sq cm
33. 33.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
34. 34.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
35. 35.A cuboid is 7 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 21 cu cm (b) 276 cu cm (c) 280 cu cm (d) 28 cu cm
36. 36.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 12 cu cm (b) 15 cu cm (c) 96 cu cm (d) 136 cu cm
37. 37.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 64 sq cm (d) 256 sq cm
38. 38.A cuboid is 10 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 95 sq cm (b) 380 sq cm (c) 190 sq cm (d) 150 sq cm
39. 39.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 10 cu cm (b) 62 cu cm (c) 15 cu cm (d) 30 cu cm
40. 40.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 726 cu cm (c) 484 cu cm (d) 33 cu cm

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