Question

A cylinder of height $90cm$ and base diameter $8cm$ is melted and recast into spheres of diameter $12cm$. Find the number of spheres.

Answer 1

Given that: for sphere $D=12cm=R=\frac{12}{2}=6cm$
for cylinder $d=8cm$ $\Rightarrow$ $r=8/2=4cm$ and $h=90cm$
Let the number of spheres made $=n$
According to the question
Volume of $n$ sphere $=$ Volume of cylinder
$\Rightarrow \pi \times \frac{4}{3}\times \pi r^2=\pi r^{2}h$
$\Rightarrow \pi \times \frac{4}{3}\pi {\left(6\right)}^3=\pi \times 4^2\times 90$
$\Rightarrow$ $n=5$ spheres