Question

The base radius and height of a right circular cone are $2cm$ and $8cm$ respectively. It is melted to change into sphere of diameter $2cm$ each. Find the number of sphere formed.

Answer 1

Step 1: Given information

Cylinder:

Radius$r=2cm$

Height$h=8cm$

Sphere:

Radius

$$\begin{gathered} r\text{'}=\frac{Diameter}{2} \\ =\frac{2}{2} \\ =1cm \end{gathered}$$

Step 2: Find the number of spheres formed.

The volume of cylinder $=$ Volume of sphere

$$\begin{gathered} \frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\mathrm{n}\times \frac{4}{3}{\mathrm{\pi r}}^3 \\ \Rightarrow \frac{1}{3}\times 2\times 2\times 8=\mathrm{n}\times \frac{4}{3}\times {\left(1\right)}^3 \\ \Rightarrow \frac{32}{3}=\mathrm{n}\times \frac{4}{3} \\ \Rightarrow \mathrm{n}=\frac{32}{3}\times \frac{3}{4} \\ \Rightarrow \mathrm{n}=8 \end{gathered}$$

Hence, the number of spheres formed.is $8$