Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 859 · 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 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
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
3. 3.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) 25 times (c) 10 times (d) 125 times
4. 4.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
5. 5.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
6. 6.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 100 sq cm (c) 25 sq cm (d) 150 sq cm
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
8. 8.A cuboid is 5 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 158 cu cm (b) 15 cu cm (c) 16 cu cm (d) 120 cu cm
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
15. 15.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
17. 17.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
18. 18.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
19. 19.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 8 times (d) 2 times
20. 20.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
21. 21.A cuboid is 11 cm long, 10 cm wide and 2 cm high. What is its volume? (a) 110 cu cm (b) 23 cu cm (c) 304 cu cm (d) 220 cu cm
22. 22.A cuboid is 7 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 41 sq cm (b) 164 sq cm (c) 82 sq cm (d) 42 sq cm
23. 23.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 108 cu cm (b) 12 cu cm (c) 13 cu cm (d) 72 cu cm
24. 24.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
25. 25.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 384 sq cm (c) 512 sq cm (d) 64 sq cm
26. 26.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 600 cu cm
27. 27.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
28. 28.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
29. 29.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 729 cu cm (d) 324 cu cm
30. 30.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
31. 31.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 41 sq cm (b) 42 sq cm (c) 82 sq cm (d) 164 sq cm
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) 9 times (c) 6 times (d) 3 times
33. 33.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 217 sq cm (c) 36 sq cm (d) 216 sq cm
34. 34.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 9 cu cm (b) 20 cu cm (c) 48 cu cm (d) 10 cu cm
35. 35.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
36. 36.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
37. 37.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) 125 times (c) 10 times (d) 25 times
38. 38.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
39. 39.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
40. 40.A cuboid is 5 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 224 sq cm (b) 56 sq cm (c) 80 sq cm (d) 112 sq cm

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