Question

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed. [CBSE 2014]

Answer 1

Let the number of such cones formed be n
Now, Volume of solid metallic sphere = Volume of n solid cones

$$\begin{gathered} \Rightarrow \frac{4}{3}\times \frac{22}{7}\times {\left(5.6\right)}^3=n\times \frac{1}{3}\times \frac{22}{7}\times {\left(2.8\right)}^2\times 3.2 \\ \Rightarrow 4\times {\left(5.6\right)}^3=n\times {\left(2.8\right)}^2\times 3.2 \\ \Rightarrow n=28 \end{gathered}$$