Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 887 · 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) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
2. 2.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 33 cu cm (d) 1331 cu cm
3. 3.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) 8 times (d) 2 times
4. 4.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
5. 5.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
6. 6.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) 27 times (c) 6 times (d) 9 times
7. 7.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
8. 8.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 120 sq cm (b) 296 sq cm (c) 148 sq cm (d) 74 sq cm
9. 9.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
10. 10.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 384 sq cm (d) 512 sq cm
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
13. 13.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
14. 14.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
15. 15.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 144 sq cm (d) 217 sq cm
16. 16.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) 4 times (d) 16 times
17. 17.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 384 cu cm (d) 256 cu cm
18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
19. 19.If the radius of a circle 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
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
22. 22.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
23. 23.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 100 cu cm (c) 150 cu cm (d) 15 cu cm
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
26. 26.A cuboid is 10 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 112 cu cm (b) 60 cu cm (c) 20 cu cm (d) 15 cu cm
27. 27.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
28. 28.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 125 sq cm (d) 25 sq cm
29. 29.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
30. 30.A cuboid is 10 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 21 cu cm (b) 240 cu cm (c) 268 cu cm (d) 30 cu cm
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
32. 32.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 10 cu cm (b) 118 cu cm (c) 70 cu cm (d) 14 cu cm
33. 33.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 10 cu cm (b) 6 cu cm (c) 30 cu cm (d) 62 cu cm
34. 34.A cuboid is 7 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 105 sq cm (b) 142 sq cm (c) 71 sq cm (d) 284 sq cm
35. 35.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 26 sq cm (b) 24 sq cm (c) 104 sq cm (d) 52 sq cm
36. 36.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
37. 37.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) 9 times (d) 6 times
38. 38.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
39. 39.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
40. 40.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm

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