Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 328 · 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 radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
2. 2.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
3. 3.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
5. 5.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
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
7. 7.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
8. 8.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) 3 times (c) 27 times (d) 6 times
9. 9.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
10. 10.A cuboid is 12 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 320 sq cm (b) 96 sq cm (c) 80 sq cm (d) 160 sq cm
11. 11.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
12. 12.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
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
14. 14.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
15. 15.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) 16 times (c) 4 times (d) 8 times
16. 16.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
17. 17.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
18. 18.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 144 cu cm (d) 217 cu cm
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
20. 20.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 80 sq cm (b) 20 sq cm (c) 16 sq cm (d) 40 sq cm
21. 21.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
22. 22.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 726 cu cm
23. 23.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
24. 24.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 36 sq cm (d) 54 sq cm
25. 25.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 8 cu cm (c) 88 cu cm (d) 48 cu cm
26. 26.A cuboid is 12 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 300 sq cm (c) 216 sq cm (d) 600 sq cm
27. 27.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
28. 28.A cuboid is 11 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 22 cu cm (b) 220 cu cm (c) 23 cu cm (d) 304 cu cm
29. 29.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 64 cu cm (d) 12 cu cm
30. 30.A cuboid is 7 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 18 cu cm (b) 196 cu cm (c) 28 cu cm (d) 210 cu cm
31. 31.A cuboid is 9 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 135 sq cm (b) 87 sq cm (c) 348 sq cm (d) 174 sq cm
32. 32.A cuboid is 8 cm long, 7 cm wide and 3 cm high. What is its total surface area? (a) 168 sq cm (b) 101 sq cm (c) 404 sq cm (d) 202 sq cm
33. 33.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
34. 34.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
35. 35.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 512 cu cm (d) 24 cu cm
36. 36.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 240 cu cm (b) 20 cu cm (c) 248 cu cm (d) 24 cu cm
37. 37.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
38. 38.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 6 cu cm (d) 16 cu cm
39. 39.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) 5 times (c) 2 times (d) 4 times
40. 40.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) 125 times (c) 5 times (d) 25 times

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