Question

Question 12
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2cm$ and height $16cm$. the diameter of each sphere is
(A) $4cm$
(B) $3cm$
(C) $2cm$
(D) $6cm$

Answer 1

Option (C) is correct.

Given, diameter of the cylinder $=2cm$
$\therefore$ Radius $=1cm$ and height of the cylinder $=16cm$ $[\because Diameter=2\times radius]$

$\because$ Volume of cylinder $=\pi \times (radius{)}^2\times height$
$\therefore$ Volume of the given cylinder $=\pi \times (1{)}^{2}16=16\pi c{m}^3$

Now, let the radius of the solid sphere $=rcm$
Then, its volume $=\frac{4}{3}\pi r^{3}c{m}^3$ [ Volume of sphere $=\frac{4}{3}\times \pi \times \left(radius{)}^3\right]$

According to the question,
Volume of the twelve solid sphere = Volume of cylinder
$\Rightarrow 12\times \frac{4}{3}\pi r^3=16\pi r^3=1\Rightarrow r=1cm$
Therefore diameter of each sphere, $d=2r=2\times 1=2cm$

Hence the required diameter of each sphere is $2cm$