Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 978 · 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 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
2. 2.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 4 times (d) 2 times
3. 3.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
4. 4.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 33 sq cm (b) 66 sq cm (c) 36 sq cm (d) 132 sq cm
5. 5.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
6. 6.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) 8 times (d) 4 times
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
11. 11.If the side of a square 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
12. 12.A cuboid is 6 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 72 sq cm (b) 54 sq cm (c) 216 sq cm (d) 108 sq cm
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
15. 15.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
16. 16.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
17. 17.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
18. 18.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
19. 19.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) 44 sq cm (d) 88 sq cm
20. 20.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
21. 21.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 256 cu cm (d) 384 cu cm
22. 22.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
23. 23.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
24. 24.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
25. 25.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 21 cu cm (c) 294 cu cm (d) 196 cu cm
26. 26.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
27. 27.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 162 sq cm (d) 126 sq cm
28. 28.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 36 cu cm (d) 27 cu cm
29. 29.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
30. 30.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 576 sq cm (d) 1728 sq cm
31. 31.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
32. 32.A cuboid is 9 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 21 cu cm (b) 243 cu cm (c) 27 cu cm (d) 270 cu cm
33. 33.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) 9 times (c) 3 times (d) 27 times
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
35. 35.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) 10 times (c) 25 times (d) 5 times
36. 36.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 32 sq cm (c) 65 sq cm (d) 64 sq cm
37. 37.A cuboid is 12 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 18 cu cm (b) 96 cu cm (c) 160 cu cm (d) 48 cu cm
38. 38.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
39. 39.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) 10 times (c) 25 times (d) 125 times
40. 40.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 65 cu cm (d) 64 cu cm

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