Question

A cylinder is made of glass, whose radius and height are $4cm$ and $10cm$ respectively. By melting it, how many sphere with radii $2cm$ each can be recasted?

Answer 1

Given, for a cylinder Radius $=4cm$
And height $=10cm$
Volume $=\pi r^{2}h$
$=\pi \times 4\times 4\times 10{cm}^3$
Again the radius of a sphere recasted ( $r$ )
$=2cm$.
Volume of sphere $=\frac{4}{3}\pi r^2$
$=\frac{4}{3}\times \pi \times (2{)}^3$
Let the number of sphere recasted be $n$, then Volume of the cylinder $=n\times$
Volume of sphere $n=\frac{\text{Volume of cylinder}}{\text{Volume of a sphere}}$
$=\frac{\pi \times 4\times 4\times 10}{\frac{4}{3}\times \pi \times 2\times 2\times 2}$
$\begin{array}{c}=\frac{4\times 4\times 10\times 3}{4\times 4\times 2}\\ =15\end{array}$
Hence, the number of sphere recasted = 15