Question

A solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed. (Use $\mathrm{\pi }=\frac{22}{7}$ )

Answer 1

Let there are n number of small solid cones.
Now, Volume of solid sphere = n ⨯ volume of one small cone
$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }{R}^3=n\times \frac{1}{3}\mathrm{\pi }{r}^{2}h \\ \Rightarrow 4{\left(10.5\right)}^3=n\times {\left(3.5\right)}^2\times 3 \\ \Rightarrow 4{\left(10.5\right)}^3=n\times {\left(3.5\right)}^2\times 3 \\ \Rightarrow n=126 \end{gathered}$$
Hence, there are 126 number of small solid cones.