Question

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

Answer 1

Internal radius of hollow sphere (r) = 2 cm
external radius of hollow sphere( R )= 4 cm.

Volume of the Hollow sphere $=\frac{4}{3}\pi (R^3-r^3)$

$=\frac{4}{3}\pi (4^3-2^3)$

$=\frac{4}{3}\pi (64-8)$

$=\frac{4}{3}\pi \left(56\right)c{m}^3$

radius of the cone$\left(r_1\right)$= 4 cm

Let the height of the cone be h cm.
Volume of the cone $=\frac{1}{3}\pi (r_1{)}^{2}h=\frac{1}{3}\pi \times 4^{2}h=\frac{16}{3}\pi h$

Volume of the cone = Volume of the hollow sphere

$\frac{16}{3}\pi h=\frac{4}{3}\pi \left(56\right)$

$16h=4\times 56$

$h=\frac{4\times 56}{16}=14cm$

Hence, the height of the cone is 14 cm.

Let the slant height be l
Therefore,

$L^2=r_{cone}^2+h^2=4^2+{14}^2=160+0196=212$

$L=14.56cm$

Slant height