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A rectangular sheet of paper is rolled along its length to make a cylinder. The sheet is 33 cm long 32cm wide. A circular sheet of paper is attached to the bottom of the cylinder formed. Find the capacity of the cylinder so formed.

A rectangular sheet of paper is rolled along its length to make a cylinder. The sheet is 33 cm long 32cm wide. A circular sheet of paper is attached to the bottom of the cylinder formed. Find the capacity of the cylinder so formed.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
20 days ago
Hint: A rectangular sheet is rolled to make a cylinder along its length. Then the length of the rectangle becomes the length of the cylinder. And wide become the perimeter of the circle hence l=33cm and p=32cm from p we can calculate the radius of the circle as p=2πr=32cm,now we know length and radius of cylinder then volume of cylinder is equal to πr2l. Then substituting π=227 we will calculate the required value. Complete step by step solution: A rectangular sheet is rolled to make a cylinder along its length. Then length of the rectangle is become the length of the cylinder and wide become the perimeter of the circle So, length cylinder= l=33cm And perimeter= 32cm p=2πr=32cm So, r=16πcm Now, we know that Volume of cylinder =πr2l Substituting l=33cm and r=16πcmthen Volume =π×(16π)2×33cm3 V=256×33πcm3 Substituting π=227 V=2688cm3=2.688liter Note: If a sheet is folded along with width then its length becomes the perimeter of the circle. Formulas must be remembered: the live perimeter is p=2πrand volume πr2l. The Units of the quantities must be mentioned and all the units must be the same. 1000cubic cm = 1 liter

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