Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 304 · 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.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 150 cu cm (b) 16 cu cm (c) 12 cu cm (d) 108 cu cm
2. 2.A cuboid is 12 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 792 sq cm (b) 504 sq cm (c) 396 sq cm (d) 198 sq cm
3. 3.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
5. 5.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 576 cu cm (c) 36 cu cm (d) 864 cu cm
6. 6.A cuboid is 12 cm long, 9 cm wide and 5 cm high. What is its volume? (a) 426 cu cm (b) 108 cu cm (c) 26 cu cm (d) 540 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) 5 times (b) 10 times (c) 125 times (d) 25 times
8. 8.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) 4 times (c) 8 times (d) 16 times
9. 9.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
10. 10.A cuboid is 11 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 231 cu cm (b) 262 cu cm (c) 21 cu cm (d) 33 cu cm
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
12. 12.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
13. 13.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) 5 times (c) 4 times (d) 8 times
14. 14.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 16 cu cm (b) 136 cu cm (c) 8 cu cm (d) 80 cu cm
15. 15.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
17. 17.A cuboid is 10 cm long, 7 cm wide and 8 cm high. What is its volume? (a) 560 cu cm (b) 70 cu cm (c) 412 cu cm (d) 25 cu cm
18. 18.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) 4 times (d) 2 times
19. 19.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
20. 20.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) 3 times (c) 6 times (d) 27 times
21. 21.A cuboid is 8 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 180 sq cm (b) 144 sq cm (c) 90 sq cm (d) 360 sq cm
22. 22.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
24. 24.A cuboid is 9 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 576 sq cm (b) 208 sq cm (c) 832 sq cm (d) 416 sq cm
25. 25.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) 25 times (c) 10 times (d) 5 times
26. 26.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
27. 27.A cuboid is 6 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 120 sq cm (b) 60 sq cm (c) 72 sq cm (d) 240 sq cm
28. 28.A cuboid is 11 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 165 sq cm (b) 103 sq cm (c) 206 sq cm (d) 412 sq cm
29. 29.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 100 sq cm (c) 25 sq cm (d) 125 sq cm
30. 30.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) 5 times (c) 8 times (d) 4 times
31. 31.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 8 times (d) 6 times
32. 32.A cuboid is 7 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 142 cu cm (c) 105 cu cm (d) 35 cu cm
33. 33.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 64 sq cm (d) 96 sq cm
34. 34.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
35. 35.A cuboid is 7 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 11 cu cm (b) 64 cu cm (c) 14 cu cm (d) 28 cu cm
36. 36.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
37. 37.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
38. 38.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) 3 times (c) 27 times (d) 9 times
39. 39.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
40. 40.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 12 cu cm (b) 6 cu cm (c) 32 cu cm (d) 7 cu cm

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