Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 533 · 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 circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
2. 2.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 124 sq cm (b) 240 sq cm (c) 248 sq cm (d) 496 sq cm
3. 3.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 24 cu cm (d) 6 cu cm
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
6. 6.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 1728 cu cm (c) 576 cu cm (d) 36 cu cm
7. 7.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
8. 8.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 126 sq cm (b) 162 sq cm (c) 81 sq cm (d) 324 sq cm
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
10. 10.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
11. 11.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 36 cu cm (c) 27 cu cm (d) 9 cu cm
12. 12.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 9 sq cm (c) 54 sq cm (d) 27 sq cm
13. 13.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) 5 times (d) 25 times
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
15. 15.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
16. 16.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) 3 times (d) 6 times
17. 17.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) 3 times (c) 9 times (d) 27 times
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 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.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) 2 times (c) 4 times (d) 5 times
21. 21.A cuboid is 7 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 84 cu cm (b) 122 cu cm (c) 28 cu cm (d) 14 cu cm
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
23. 23.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) 64 times (c) 16 times (d) 8 times
24. 24.A cuboid is 9 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 336 sq cm (b) 84 sq cm (c) 168 sq cm (d) 108 sq cm
25. 25.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
26. 26.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) 8 times (c) 16 times (d) 64 times
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
28. 28.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
29. 29.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
30. 30.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
31. 31.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 100 sq cm (b) 160 sq cm (c) 80 sq cm (d) 320 sq cm
32. 32.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 8 times (d) 2 times
33. 33.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
34. 34.A cuboid is 11 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 480 sq cm (b) 704 sq cm (c) 240 sq cm (d) 960 sq cm
35. 35.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
36. 36.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 144 cu cm (c) 216 cu cm (d) 18 cu cm
37. 37.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
38. 38.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 294 sq cm (c) 49 sq cm (d) 196 sq cm
39. 39.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
40. 40.A cuboid is 12 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 96 cu cm (c) 18 cu cm (d) 160 cu cm

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