Question

A hollow sphere of internal and external radii $2cm$ and $4cm$ respectively is melted into a cone of base radius $4cm$. Find the height and slant height of the cone.

Answer 1

Given:

hollow sphere of internal and external radii 2cm and 4 cm

Hollow sphere melted into a cone of base radius 4 cm.

We know,

Volume of sphere $=V_s=\frac{4}{3}\pi (R_e^3-R_i^3)$

Volume of cone $=V_c=\frac{1}{3}\pi r^{2}h$

Now comparing both volume,

$V_c=V_s\Rightarrow \frac{1}{3}\pi 4^{2}h=\frac{4}{3}\pi (4^3-2^3)$

Solving this we get hight,

$\Rightarrow h=14cm$

Slant height of the cone is,

$l=\sqrt{{14}^2+4^2}=14.56cm$

Hence, the height and slant height of the cone is 14cm and 14.56cm respectively.