Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 444 · 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) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq 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) 3 times (b) 6 times (c) 9 times (d) 27 times
3. 3.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
4. 4.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 16 sq cm (d) 96 sq cm
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
6. 6.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
7. 7.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
8. 8.A cuboid is 11 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 66 cu cm (b) 472 cu cm (c) 660 cu cm (d) 27 cu cm
9. 9.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 486 sq cm (c) 729 sq cm (d) 81 sq cm
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
11. 11.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
12. 12.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
14. 14.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 150 sq cm (d) 100 sq cm
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
16. 16.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
17. 17.A cuboid is 7 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 428 sq cm (b) 210 sq cm (c) 107 sq cm (d) 214 sq cm
18. 18.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
19. 19.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 1728 cu cm (c) 864 cu cm (d) 36 cu cm
20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
21. 21.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 324 cu cm (d) 729 cu cm
22. 22.A cuboid is 12 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 224 sq cm (b) 112 sq cm (c) 448 sq cm (d) 192 sq cm
23. 23.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
24. 24.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 64 cu cm (b) 112 cu cm (c) 8 cu cm (d) 14 cu cm
25. 25.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
26. 26.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
27. 27.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
28. 28.A cuboid is 8 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 40 cu cm (b) 160 cu cm (c) 17 cu cm (d) 184 cu cm
29. 29.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 75 sq cm (b) 300 sq cm (c) 108 sq cm (d) 150 sq cm
30. 30.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 125 cu cm (c) 15 cu cm (d) 150 cu cm
31. 31.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) 2 times (d) 8 times
32. 32.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
33. 33.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
34. 34.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
35. 35.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 8 times (c) 4 times (d) 6 times
36. 36.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
37. 37.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) 125 times (c) 10 times (d) 25 times
38. 38.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
39. 39.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 164 cu cm (b) 17 cu cm (c) 120 cu cm (d) 12 cu cm
40. 40.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm

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