question_answer

A metallic solid sphere of radius \[10.5\text{ }cm\] is melted and recasted into smaller solid cones, each of radius \[3.5\text{ }cm\] and height\[3\text{ }cm\]. How many cones will be made?

Answer:

Volume of metal in cones = Volume of solid sphere

Let n = number of cones

\[\text{n }\!\!\times\!\!\text{ volume of each cone=volume of solid sphere}\]

\[\text{n=}\frac{Volume\,\,of\,\,sphere}{Volume\,\,of\,\,cone}=\frac{\frac{4}{3}\pi r_{sp}^{3}}{\frac{1}{3}\pi r_{cone}^{2}h}\]

\[=\frac{4\times 10.5\times 10.5\times 10.5}{3.5\times 3.5\times 3}\]

\[=\frac{4\times 105\times 105\times 105\times 10\times 10}{35\times 35\times 3\times 10\times 10\times 10}=\frac{4\times 3\times 105}{10}=126\]

So, 126 cones will be made.