Question

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.

Answer 1

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 $p = 2\pi r = 32cm$,now we know length and radius of cylinder then volume of cylinder is equal to $\pi {r^2}l$. Then substituting $\pi = \dfrac{{22}}{7}$ 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
$p = 2\pi r = 32cm$
So, $r = \dfrac{{16}}{\pi }cm$
Now, we know that
Volume of cylinder =$\pi {r^2}l$
Substituting l=33cm and $r = \dfrac{{16}}{\pi }cm$then
Volume =$\pi \times {\left( {\dfrac{{16}}{\pi }} \right)^2} \times 33c{m^3}$
$V = \dfrac{{256 \times 33}}{\pi }c{m^3}$
Substituting $\pi = \dfrac{{22}}{7}$

$V = 2688c{m^3} = 2.688liter$

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 $p = 2\pi r$and volume $\pi {r^2}l$. The Units of the quantities must be mentioned and all the units must be the same. 1000cubic cm = 1 liter