Question

If a square sheet with side 2π units is rolled into a cylinder along one of its sides, the volume of the cylinder so obtained will be _____ cubic units.

Answer 1

We know that when we roll a square over any of its sides, it forms a cylinder.


The height of the cylinder is equal to the length of the side of the sqaure.

Given:
Side of square = 2π units
⇒ Height of cylinder = 2π units

Also, the side of the square is the circumference of the circular base of the cylinder.
Let the radius of the cylinder be r.

Circumference of a circle = 2πr

Hence, on putting the values, we get:
2πr = 2π
$\Rightarrow r=\frac{2\pi }{2\pi }=1\text{unit}$

We know:
$\text{Volume of cylinder}=\pi \times r^2\times h$

So, the volume of the cylinder
$=\pi \times r^2\times h$
$=\pi \times 1^2\times 2\pi$
$=2{\pi }^2\text{cubic units}$