Question

How many cones with radius $3cm$ and height $6cm$ can be formed by melting a metallic sphere with radius $9cm$.

Answer 1

Given,
Radius of sphere $\left(r\right)=9cm$
Volume of the sphere $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times 9\times 9\times 9{cm}^3$
For a cone,
Radius $\left(R\right)=3cm$
Height $\left(h\right)=6cm$
Volume of the cone $=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times 3\times 3\times 6{cm}^3$
Let the number of cones recasted be n.
$\therefore$ Volume of sphere $=n\times$
volume of a cones
$\Rightarrow \frac{4}{3}\times \frac{22}{7}\times 9\times 9\times 9=n\times \frac{1}{3}\times \frac{22}{7}\times 3\times 3\times 6$
$\begin{array}{cc}n& =\frac{\frac{4}{3}\times \frac{22}{7}\times 9\times 9\times 9}{\frac{1}{3}\times \frac{22}{7}\times 3\times 3\times 6}\\ & =54\end{array}$
Hence, the number of cones recasted = 54