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A rectangular sheet of paper `30 cm xx 18 cm` can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volume of the two cylinders, thus formed. |
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Answer» Correct Answer - `5 : 3` Case I When the sheet is folded along its length: In this case, it forms a cylinder having height `h_(1) = 18cm` and the circumference of its base equal to 30 cm Let the radius of its base be `r_(1)`. Then, `2pir_(1) = 30 rArr r_(1) = (15)/(pi)` `:. V_(1) = pir_(1)^(2) h_(1) = {pi xx ((15)/(pi))^(2) xx 18} cm^(3) = (4050)/(pi) cm^(3)` Case II When the sheet is folded along its breadth: In this case, we get a cylinder having height `h_(2)` = 30 cm and the circumference of its base equal to 18 cm. Let the radius of its base be `r_(2)`. Then, `2pir_(2) = 18 rArr r_(2) = (9)/(pi)` `:. V_(2) = pi r_(2)^(2) h_(2) = {pi xx ((9)/(11))^(2) xx 30} cm^(3) = (2430)/(pi) cm^(3)` `:. (V_(1))/(V_(2)) = ((4050)/(pi) xx (pi)/(2430)) = (4050)/(2430) = (5)/(3)` |
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