Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2\ cm$ and height $16\ cm$. Find the diameter of each sphere.

Given: Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2\ cm$ and height $16\ cm$.

To do: To find the diameter of each sphere.

Solution:

Volume of the cylinder, $V_{c}=\pi r^2h$

Volume of the cylinder, $V_{c}=12\times V_{s}$              $( V_s\ is\ volume\ of\ the\ sphere)$

$\Rightarrow \pi r_{c}^2h=12\times \frac{4}{3}\pi r_{s}^3$
​
$\Rightarrow \pi \times 1^2\times 16=12\times \frac{4}{3}\pi r_{s}^3$

$\Rightarrow r_{s}^3=1$​
 
$\Rightarrow r_s=1\ cm$

$\therefore$ Diameter of the sphere, $d_s=2\times r_s=2\times1$

So, diameter of each sphere is $2\ cm$.

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Updated on: 10-Oct-2022

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