A metallic spherical shell of internal and external diameters $4\ cm$ and $8\ cm$ respectively, is melted and recast into the form of a cone with base diameter $8\ cm$. Find the height of the cone.

Given: A metallic spherical shell of internal and external diameters $4\ cm$ and $8\ cm$ respectively, is melted and recast into the form of a cone with base diameter $8\ cm$.

To do: To find the height of the cone.

Solution:

Internal radius of the spherical shell, $r=4\ cm$

External radius of the spherical shell, $=8\ cm$

Base diameter of  the cone, $d=8\ cm$

$\therefore$ Radius of the cone, $r_1=\frac{d}{2}=\frac{8}{2}=4\ cm$

Let $h$ be the height of the cone.

As given that volume of cone$=$volume of sphere

$\Rightarrow \frac{1}{3}\pi r_{1}^2h=\frac{4}{3}\pi [R^3−r^3]$

$\Rightarrow 16h=4[4^3-2^3]$

$\Rightarrow 4h=56$

$\Rightarrow h=14\ cm$

Thus, height of the cone is $14\ cm$.
 

Updated on: 10-Oct-2022

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