Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 103 · 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.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
2. 2.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 400 sq cm (c) 1000 sq cm (d) 100 sq cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
4. 4.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
5. 5.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) 125 times (c) 25 times (d) 5 times
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
7. 7.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
8. 8.A cuboid is 7 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 350 cu cm (b) 22 cu cm (c) 35 cu cm (d) 310 cu cm
9. 9.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 36 cu cm
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
11. 11.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 64 cu cm (c) 65 cu cm (d) 96 cu cm
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 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) 8 times (b) 4 times (c) 16 times (d) 64 times
16. 16.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 100 sq cm (d) 150 sq cm
17. 17.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
18. 18.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 81 sq cm (d) 486 sq cm
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
21. 21.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
23. 23.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
24. 24.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
25. 25.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
26. 26.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
27. 27.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
28. 28.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 484 cu cm
29. 29.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 76 sq cm (b) 304 sq cm (c) 152 sq cm (d) 96 sq cm
30. 30.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 176 sq cm (b) 48 sq cm (c) 88 sq cm (d) 44 sq cm
31. 31.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) 5 times (c) 125 times (d) 25 times
32. 32.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
33. 33.A cuboid is 12 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 290 sq cm (b) 580 sq cm (c) 300 sq cm (d) 145 sq cm
34. 34.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
35. 35.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 51 sq cm (b) 54 sq cm (c) 204 sq cm (d) 102 sq cm
36. 36.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) 4 times (c) 2 times (d) 8 times
37. 37.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
38. 38.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 1000 cu cm (c) 30 cu cm (d) 600 cu cm
39. 39.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 220 sq cm (b) 55 sq cm (c) 75 sq cm (d) 110 sq cm
40. 40.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

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