The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is:$( A) \ 3$
$( B) \ 5$
$( C) \ 4$
$( D) \ 6$

Given: Height of the cylinder$=45\ cm$ and diameter of the cylinder$=4cm$, diameter of the sphere$=6\ cm$.


To do: To find the number of solid spheres.

Solution: Let r and h be the radius and the height of the cylinder, respectively. 

Diameter of the cylinder$=\ 4\ cm$

Radius of the cylinder, $r\ =\ \frac{4}{2} =2\ cm$

Height of the cylinder, $h\ =\ 45\ cm$ 

Volume of the solid cylinder $=\pi r^{2} h=\ \pi \times 2^{2} \times 45=180\pi \ cm^{2}$

diameter of the solid sphere$=6\ cm$

Radius of the solid sphere, $R=\frac{6}{2} =3\ cm$

Volume of each solid sphere$=\frac{4}{3} \pi R^{3}$

$=\frac{4}{3} \pi 3^{3}$

$=\frac{4}{3} \pi \times 27$

$=36\mathbf{\pi }$

let n be the number of solid sphere, formed after melting the metallic cylinder,

then,

$n\times 36\pi =180\pi $

$n=\frac{180\pi }{36\pi } =5$

Thus, Option $( B)$  is correct.

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Updated on: 10-Oct-2022

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