Question

A metallic sphere of radius $10.5$ cm is melted and then recast into small cones each of radius $3.5$ cm and height $3$ cm Find the number of cones thus formed

• A. $216$
• B. $621$$
• C. $162$
• D. $126$

Answer 1

The correct option is D $126$

Volume of sphere melted$=\frac{4}{3}\pi R^3=\frac{4}{3}\pi \times {10.5}^3$
Volume of each cone formed = $\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \times {\left(3.5\right)}^2\times 3$
$\therefore$ Number of cones obtained = $\frac{Volumeofthespheremelted}{Volumeofeachconeformed}$
$=\frac{\left(\frac{4}{3}\right)\pi \times {\left(10.5\right)}^3}{\left(\frac{1}{3}\right)\times \pi \times {\left(3.5\right)}^2\times 3}=126$