Question

$504$ cones, each of diameter $3.5$ cm and height $3$ cm, are melted and recast into a metallic sphere. Find the diameter of the sphere . Use $\pi =\frac{22}{7}$.

Answer 1

Given $r=\frac{3.5}{2}$ cm and $h=3cm$

Volume of cone $=\frac{1}{3}\pi r^{2}h$

Volume of cone $=\frac{1}{3}\pi {\left(\frac{3.5}{2}\right)}^2\times 3$=$\frac{1}{3}\times \frac{22}{7}\times \frac{3.5}{2}\times \frac{3.5}{2}\times 3=\frac{19.25}{2}c{m}^3$

Volume of $504$ cones $=504\times \frac{19.25}{2}=4851c{m}^3$

Volume of sphere $=\frac{4}{3}\pi r^3$

Cones are melted and recast in sphere

$\therefore \frac{4}{3}\times \frac{22}{7}{r}^3=4851$

$\Rightarrow r^3=\frac{4851\times 21}{88}=\frac{441\times 21}{8}$

$\Rightarrow r=\frac{21}{2}=10.5cm$

Diameter of sphere $=2\times 10.5=21cm$