Question

The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5cm respectively. If it is melted and recast into a solid cylinder of height $2\frac{2}{3}$cm. Find the diameter of the cylinder.

Answer 1

In the given problem, we have a spherical shell which is remolded into a solid cylinder. So here, we first find the volume of the spherical shell.

We are given that,

Radius of internal surface of the spherical shell = 3 cm

Radius of external surface of the spherical shell = 5 cm

So,

The volume of the spherical shell =

Where, R = external radius

r = internal radius

So,

Volume of the shell =

Next we find the volume of the cylinder.

Height of the cylinder =

Let us take the radius of the cylinder as r cm.

So,

Volume of the cylinder =

Now, according to the problem, the volume of shell will be equal to the volume of the solid cylinder. So, we get

Volume of spherical shell = Volume of cylinder

Since, the radius is 7 cm; the diameter of the cylinder will be 14 cm.

Therefore, the diameter of the cylinder is.