Question

if the radius and height of a ridht circular cylinder will be double then how many times the volume of new cylinder will be the volume of the original right circular cylinder​

Answer 1

To find:-

How many times will the volume of a cylinder increase if the height and radius is doubled.

Assumption:-

Let the radius and height of first cylinder be r and h

Radius and height of second cylinder = 2r and 2h

Solution:-

For the first cylinder,

Radius = r units.

Height = h units.

Volume of a cylinder = $\pi \times {r}^{2} \times h$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$= $\pi {r}^{2} h$ cubic units.

For the second cylinder,

Radius = 2r

Height = 2h

Volume of cylinder = $\pi {(2r)}^{2} 2h$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ = $\pi {4r}^{2} 2h$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ = $8\pi {r}^{2} h$ cubic units.

To find how many times the volume of the original cylinder becomes when the radius and height are doubled, We need to divide the volume of 2nd second cylinder by volume of 1st cylinder.

= $\frac{8\pi {r}^{2} h}{\pi {r}^{2} h}$

= 8 times. ${\boxed{Answer}}$

Therefore the volume of the original cylinder increases by 8 times when it's height and radius are doubled.