The radii of internal and external surface of a hollow spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.
We have,
The internal base radius of spherical shell, r1 = 3 cm,
The external base radius of spherical shell, r2 = 5 cm and
The base radius of solid cylinder, r = 7 cm
Let the height of the cylinder be h
As,
The hollow spherical shell is melted into a solid cylinder;
So,
Volume of solid cylinder = Volume of spherical shell
⇒ πr2h =
⇒ πr2h =
⇒ r2h =
⇒ 49 × h = (125−27)
⇒ h = × 9849
Therefore,
h =
So, the height of the cylinder is .