Question

Of a hollow sphere of internal and external diameter are 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm. Find height of cone

Answer 1

ANSWER:-

Given:

•Internal diameter of hollow sphere is 4cm.

•Internal radius of hollow sphere is 4/2

=)(r)=2cm

•External diameter of hollow sphere is 8cm.

•External radius of hollow sphere is 8/2

=)(R)=4cm

According to the question:

•Let the height of the cone be h cm.

Volume of the hollow sphere= volume of cone

$= > \frac{4}{3} \pi( {R}^{3} - {r}^{3} ) = \frac{1}{3} \pi {r}^{2} h \\ \\ = > \frac{4}{3} \pi( {4}^{3} - {2}^{3} ) = \frac{1}{3} \pi {4}^{2} h \\ \\ = > 4( {4}^{3} - {2}^{3} ) = {4}^{2} \times h \\ \\ = > 64 - 8 = 4 \times h \\ \\ = > 56 = 4h \\ \\ = > h = \frac{56}{4} \\ \\ = > h = 14cm$

Thus,

The height of the cone is 14cm.

Hope it helps ☺️