Question

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

Answer 1

Answer :

➥ The Height of a cylindrical tank = h/2 i.e, the height will be halved.

Given :

➤ Lateral surface area of both the cylinder are equal.

To Find :

➤ Height will be ?

Solution :

Let ,

The radius of a cylinder be "r" and the height of a cylinder be "h".

Lateral surface area = 2πrh

When radius is doubled then radius = 2r

So ,

Lateral surface area of a cylinder = 2π2rh'

Lateral surface area of a cylinder = New lateral surface area of a cylinder.

It is given that lateral surface area of both the cylinder are equal.

$\tt{: \implies \cancel{2} \cancel{\pi} 2 \cancel{r}h' = \cancel{2} \cancel{\pi} \cancel{r}h}$

$\tt{: \implies 2h' = h}$

$\bf{: \implies \underline{\:\:\underline{\purple{\:\:h' = \dfrac{h}{2}\:\: }}\:\:}}$

Hence, the height will be halved.

Answer 2

solution:

$\longrightarrow\underline{\underline{\red{\sf{ \: h = \frac{1}{2} (half) }}}} \sf$

$\tt {\pink{Given}}\begin{cases} \sf{\green{radius = h}}\\ \sf{\blue{radius \: when \: doubled = 2h}}\\ \sf{\orange{lateral \: surface \: area=2πrh}}\\ \sf{\red{height=?}}\end{cases}$

_________________________

so,

$\sf \: lateral \: surface \: area \: of \: cylinder = 2π2rh$

$\sf \: lateral \: surface \: area \: of \: new \: cylinder = 2πrh$

$\sf \: given = lateral \: surface \: area \: of \: \: both \\ \sf cylinders \: is \: equal$

therefore,

$\sf \longrightarrow2π2rh = 2πrh$

$\sf \longrightarrow2h = h(as \: 2 , π \: and \: r \: </u><u>are</u><u> \: cancelled)$

$\sf \longrightarrow \: h = \frac{h}{2}$

$∴\underline{\underline{\red{\sf{h = \frac{h}{2} }}}}$