Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 496 · 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 12 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 264 sq cm (b) 66 sq cm (c) 132 sq cm (d) 72 sq cm
2. 2.If the radius of a circle 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
3. 3.A cuboid is 9 cm long, 7 cm wide and 5 cm high. What is its total surface area? (a) 572 sq cm (b) 286 sq cm (c) 315 sq cm (d) 143 sq cm
4. 4.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 1000 sq cm (c) 400 sq cm (d) 100 sq cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
7. 7.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
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
11. 11.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
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
13. 13.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
14. 14.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
15. 15.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
16. 16.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
17. 17.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) 4 times (c) 2 times (d) 5 times
18. 18.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
19. 19.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
20. 20.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
21. 21.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
22. 22.A cuboid is 12 cm long, 11 cm wide and 2 cm high. What is its total surface area? (a) 178 sq cm (b) 264 sq cm (c) 712 sq cm (d) 356 sq cm
23. 23.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) 125 times (c) 10 times (d) 25 times
24. 24.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 16 cu cm (b) 10 cu cm (c) 90 cu cm (d) 146 cu cm
25. 25.A cuboid is 11 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 580 sq cm (b) 264 sq cm (c) 145 sq cm (d) 290 sq cm
26. 26.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 512 sq cm (c) 256 sq cm (d) 64 sq cm
27. 27.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 484 cu cm
28. 28.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
29. 29.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) 3 times (c) 27 times (d) 6 times
30. 30.A cuboid is 11 cm long, 8 cm wide and 5 cm high. What is its total surface area? (a) 366 sq cm (b) 183 sq cm (c) 732 sq cm (d) 440 sq cm
31. 31.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
32. 32.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 24 cu cm (d) 256 cu cm
33. 33.A cuboid is 7 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 14 cu cm (b) 100 cu cm (c) 13 cu cm (d) 56 cu cm
34. 34.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
35. 35.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 144 sq cm (c) 864 sq cm (d) 1728 sq cm
36. 36.A cuboid is 11 cm long, 9 cm wide and 3 cm high. What is its total surface area? (a) 297 sq cm (b) 636 sq cm (c) 318 sq cm (d) 159 sq cm
37. 37.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 27 cu cm (c) 729 cu cm (d) 486 cu cm
38. 38.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
39. 39.A cuboid is 11 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 139 sq cm (b) 198 sq cm (c) 278 sq cm (d) 556 sq cm
40. 40.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm

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