Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 758 · 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) 25 times (b) 5 times (c) 10 times (d) 125 times
2. 2.A cuboid is 10 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 166 sq cm (b) 332 sq cm (c) 360 sq cm (d) 664 sq cm
3. 3.A cuboid is 9 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 27 cu cm (b) 174 cu cm (c) 17 cu cm (d) 135 cu cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
5. 5.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
6. 6.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 12 cu cm (d) 65 cu cm
7. 7.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
9. 9.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
10. 10.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
11. 11.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) 27 times (c) 9 times (d) 3 times
12. 12.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 110 cu cm (b) 15 cu cm (c) 13 cu cm (d) 75 cu cm
13. 13.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
14. 14.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
15. 15.A cuboid is 10 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 160 cu cm (b) 50 cu cm (c) 17 cu cm (d) 100 cu cm
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
17. 17.A cuboid is 7 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 324 sq cm (b) 162 sq cm (c) 126 sq cm (d) 81 sq cm
18. 18.A cuboid is 6 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 20 cu cm (b) 30 cu cm (c) 270 cu cm (d) 258 cu cm
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
21. 21.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 72 sq cm (b) 124 sq cm (c) 248 sq cm (d) 62 sq cm
22. 22.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
23. 23.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 104 cu cm (b) 13 cu cm (c) 60 cu cm (d) 30 cu cm
24. 24.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) 3 times (c) 9 times (d) 6 times
25. 25.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) 8 times (c) 4 times (d) 6 times
26. 26.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
27. 27.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) 3 times (d) 27 times
28. 28.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
29. 29.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
31. 31.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
32. 32.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
33. 33.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 36 sq cm (d) 144 sq cm
34. 34.A cuboid is 11 cm long, 8 cm wide and 9 cm high. What is its volume? (a) 792 cu cm (b) 518 cu cm (c) 88 cu cm (d) 28 cu cm
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
36. 36.A cuboid is 9 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 54 sq cm (b) 51 sq cm (c) 102 sq cm (d) 204 sq cm
37. 37.A cuboid is 10 cm long, 9 cm wide and 9 cm high. What is its total surface area? (a) 522 sq cm (b) 1044 sq cm (c) 810 sq cm (d) 261 sq cm
38. 38.A cuboid is 9 cm long, 8 cm wide and 6 cm high. What is its total surface area? (a) 696 sq cm (b) 432 sq cm (c) 348 sq cm (d) 174 sq cm
39. 39.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 162 sq cm (b) 324 sq cm (c) 108 sq cm (d) 81 sq cm
40. 40.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 256 cu cm (c) 384 cu cm (d) 24 cu cm

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