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 $\pi ={\displaystyle \frac{22}{7}}$ 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, $r={\displaystyle \frac{16}{\pi }}cm$
Now, we know that
Volume of cylinder =$\pi r^{2}l$
Substituting l=33cm and $r={\displaystyle \frac{16}{\pi }}cm$then
Volume =$\pi \times {\left({\displaystyle \frac{16}{\pi }}\right)}^2\times 33c{m}^3$
$V={\displaystyle \frac{256\times 33}{\pi }}c{m}^3$
Substituting $\pi ={\displaystyle \frac{22}{7}}$

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

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