Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 187 · 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.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
2. 2.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 124 sq cm (b) 240 sq cm (c) 496 sq cm (d) 248 sq cm
3. 3.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 96 sq cm (d) 97 sq cm
4. 4.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 48 cu cm (b) 13 cu cm (c) 92 cu cm (d) 6 cu cm
5. 5.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
6. 6.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) 25 times (c) 125 times (d) 10 times
7. 7.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
8. 8.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
9. 9.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
11. 11.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) 2 times (c) 4 times (d) 5 times
12. 12.A cuboid is 8 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 304 sq cm (b) 76 sq cm (c) 96 sq cm (d) 152 sq cm
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
14. 14.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
15. 15.A cuboid is 7 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 84 sq cm (b) 122 sq cm (c) 244 sq cm (d) 61 sq cm
16. 16.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 64 cu cm (d) 65 cu cm
17. 17.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 486 sq cm (d) 81 sq cm
18. 18.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
19. 19.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
20. 20.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) 4 times (d) 8 times
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
22. 22.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
23. 23.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
24. 24.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
25. 25.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
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) 8 times (c) 64 times (d) 16 times
27. 27.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 144 cu cm (d) 217 cu cm
28. 28.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
29. 29.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
30. 30.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 36 cu cm (d) 27 cu cm
31. 31.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
32. 32.A cuboid is 8 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 268 cu cm (b) 240 cu cm (c) 24 cu cm (d) 21 cu cm
33. 33.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 484 cu cm (c) 33 cu cm (d) 726 cu cm
34. 34.A cuboid is 12 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 160 sq cm (b) 320 sq cm (c) 336 sq cm (d) 640 sq cm
35. 35.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 11 cu cm (b) 72 cu cm (c) 6 cu cm (d) 36 cu cm
36. 36.A cuboid is 7 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 154 sq cm (b) 77 sq cm (c) 308 sq cm (d) 98 sq cm
37. 37.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
38. 38.A cuboid is 9 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 636 sq cm (b) 318 sq cm (c) 159 sq cm (d) 378 sq cm
39. 39.A cuboid is 9 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 128 sq cm (d) 180 sq cm
40. 40.A cuboid is 9 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 114 sq cm (b) 216 sq cm (c) 228 sq cm (d) 456 sq cm

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