Question

the radius of a cylindrical tank is doubled while the lateral surface area remains unchanged then the height will be​

Answer 1

The lateral surface area of a cylinder of radius $r$ and height $h$ is given by,

$\longrightarrow A=2\pi rh$

From this, height of cylinder is given by,

$\longrightarrow h=\dfrac{A}{2\pi r}$

For constant lateral surface area,

$\longrightarrow h\propto\dfrac{1}{r}$

Therefore,

$\longrightarrow \dfrac{h_2}{h_1}=\dfrac{r_1}{r_2}\quad\quad\dots(1)$

In the question the radius of a cylindrical tank is doubled, keeping its lateral surface area constant.

$\longrightarrow r_2=2r_1$

$\longrightarrow\dfrac{r_1}{r_2}=\dfrac{1}{2}$

From (1),

$\longrightarrow \dfrac{h_2}{h_1}=\dfrac{1}{2}$

$\longrightarrow\underline{\underline{h_2=\dfrac{h_1}{2}}}$

I.e., the height of the tank will be halved.