Question

If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.

Answer 1

Internal diameter of a hollow sphere = 4 cm
$\therefore Internalradius=\frac{4}{2}=2cm$
Similarly the outer radius $\left(R\right)=\frac{8}{2}=4cm$
$\therefore$ Volume of hollow sphere
$=\frac{4}{3}\pi (R^3-r^3)=\frac{4}{3}\pi [4^3-2^3]c{m}^3=\frac{4}{3}\pi [64-8]=\frac{4}{3}\pi \times 56c{m}^3=\frac{224}{3}\pi c{m}^3$
Now volume of solid cone $=\frac{224}{3}\pi c{m}^3$
Diameter of base of cone $=8cm\therefore$ Radius $=\frac{8}{2}=4$

Then height of cone $=\frac{Volume}{\frac{1}{3}\pi r^2}$

$=\frac{224\pi \times 3}{3\times \pi \times 4\times 4}$ = 14 cm