Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 629 · 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, 3 cm wide and 9 cm high. What is its total surface area? (a) 324 sq cm (b) 342 sq cm (c) 684 sq cm (d) 171 sq cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
3. 3.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 486 sq cm (c) 81 sq cm (d) 729 sq cm
4. 4.A cuboid is 12 cm long, 9 cm wide and 3 cm high. What is its volume? (a) 24 cu cm (b) 108 cu cm (c) 342 cu cm (d) 324 cu cm
5. 5.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
6. 6.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
7. 7.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 6 cu cm (b) 11 cu cm (c) 72 cu cm (d) 36 cu cm
8. 8.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) 10 times (c) 25 times (d) 125 times
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
11. 11.A cuboid is 10 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 100 cu cm (b) 17 cu cm (c) 160 cu cm (d) 20 cu cm
12. 12.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
13. 13.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
14. 14.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
15. 15.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 41 sq cm (b) 82 sq cm (c) 164 sq cm (d) 42 sq cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
17. 17.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 600 sq cm (c) 1000 sq cm (d) 100 sq cm
18. 18.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 60 sq cm (c) 112 sq cm (d) 224 sq cm
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
20. 20.A cuboid is 11 cm long, 10 cm wide and 4 cm high. What is its total surface area? (a) 776 sq cm (b) 440 sq cm (c) 194 sq cm (d) 388 sq cm
21. 21.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
22. 22.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
23. 23.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 343 sq cm (d) 294 sq cm
24. 24.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) 25 times (d) 125 times
25. 25.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
27. 27.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
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) 125 times (b) 10 times (c) 5 times (d) 25 times
29. 29.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) 8 times (c) 4 times (d) 64 times
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
31. 31.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 16 cu cm (d) 24 cu cm
32. 32.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 256 cu cm (d) 512 cu cm
33. 33.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
34. 34.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) 8 times (c) 5 times (d) 4 times
35. 35.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 217 cu cm (c) 18 cu cm (d) 216 cu cm
36. 36.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 12 cu cm (d) 64 cu cm
37. 37.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
38. 38.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
39. 39.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm

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