question_answer

A solid metallic sphere of diameter \[16\text{ }cm\] is melted and recasted into smaller solid cones, each of radius \[4\text{ }cm\] and height\[8\text{ }cm\]. Find the number of cones so formed.

Answer:

\[\text{No}\text{.}\,\,\text{of}\,\,\text{cone}\,\,\text{formed=}\frac{\text{Volume}\,\,\text{of}\,\,\text{sphere}\,\,\text{melted}}{\text{Volume}\,\,\text{of}\,\,\text{cone}}\]

\[\text{=}\frac{\frac{4}{3}\pi r_{sp}^{3}}{\frac{1}{3}\pi r_{cone}^{2}h}=\frac{4\times 8\times 8\times 8}{4\times 4\times 8}\]

\[=16\]