Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 571 · 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 diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
2. 2.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) 6 times (c) 3 times (d) 9 times
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
4. 4.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
5. 5.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
6. 6.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
7. 7.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) 5 times (c) 10 times (d) 25 times
8. 8.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
9. 9.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
10. 10.A cuboid is 8 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 106 sq cm (b) 424 sq cm (c) 212 sq cm (d) 144 sq 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) 4 times (c) 2 times (d) 8 times
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
14. 14.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
15. 15.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
16. 16.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
17. 17.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
20. 20.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 726 cu cm (d) 1331 cu cm
21. 21.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) 8 times (c) 5 times (d) 2 times
22. 22.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 484 sq cm (c) 121 sq cm (d) 726 sq cm
23. 23.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
25. 25.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 36 sq cm (d) 217 sq cm
26. 26.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
27. 27.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 42 cu cm (b) 12 cu cm (c) 6 cu cm (d) 82 cu cm
28. 28.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 512 sq cm (c) 256 sq cm (d) 384 sq cm
29. 29.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
30. 30.A cuboid is 9 cm long, 8 cm wide and 4 cm high. What is its total surface area? (a) 140 sq cm (b) 560 sq cm (c) 288 sq cm (d) 280 sq cm
31. 31.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 124 sq cm (b) 62 sq cm (c) 30 sq cm (d) 31 sq cm
32. 32.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
33. 33.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 17 cu cm (b) 164 cu cm (c) 12 cu cm (d) 120 cu cm
34. 34.A cuboid is 11 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 99 cu cm (b) 17 cu cm (c) 150 cu cm (d) 33 cu cm
35. 35.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 864 sq cm
36. 36.A cuboid is 8 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 118 sq cm (b) 472 sq cm (c) 240 sq cm (d) 236 sq cm
37. 37.A cuboid is 8 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 352 sq cm (b) 704 sq cm (c) 448 sq cm (d) 176 sq cm
38. 38.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
39. 39.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) 10 times (c) 25 times (d) 125 times
40. 40.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm

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