Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 474 · 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 7 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 91 sq cm (b) 364 sq cm (c) 147 sq cm (d) 182 sq cm
2. 2.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
3. 3.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 60 sq cm (b) 94 sq cm (c) 47 sq cm (d) 188 sq cm
4. 4.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 64 sq cm (c) 96 sq cm (d) 16 sq cm
5. 5.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
6. 6.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
8. 8.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
11. 11.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
13. 13.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 102 sq cm (b) 54 sq cm (c) 51 sq cm (d) 204 sq cm
14. 14.A cuboid is 9 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 144 sq cm (b) 106 sq cm (c) 424 sq cm (d) 212 sq cm
15. 15.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
16. 16.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 512 cu cm (d) 24 cu cm
17. 17.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
18. 18.A cuboid is 10 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 276 cu cm (b) 280 cu cm (c) 70 cu cm (d) 21 cu cm
19. 19.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 224 sq cm (b) 60 sq cm (c) 112 sq cm (d) 56 sq cm
20. 20.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
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) 5 times (c) 10 times (d) 125 times
22. 22.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
23. 23.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 6 times (d) 8 times
24. 24.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
25. 25.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 12 cu cm (b) 9 cu cm (c) 52 cu cm (d) 24 cu cm
26. 26.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) 16 times (c) 8 times (d) 64 times
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
28. 28.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 14 cu cm (b) 126 cu cm (c) 15 cu cm (d) 90 cu cm
29. 29.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 49 sq cm (d) 294 sq cm
30. 30.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
31. 31.A cuboid is 8 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 90 sq cm (b) 180 sq cm (c) 360 sq cm (d) 144 sq cm
32. 32.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
33. 33.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
35. 35.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
36. 36.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 726 sq cm (c) 1331 sq cm (d) 484 sq cm
37. 37.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
38. 38.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
39. 39.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
40. 40.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

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