According to the question it is given that,

Internal diameter of hollow sphere $=4cm$

So, the internal radius of hollow sphere $=2cm$

External diameter of hollow sphere $=8cm$

So, the external radius of hollow sphere $=4cm$

As we know that,

Volume of the hollow sphere $4/3\pi \times \left( {{4}^{3}}-{{2}^{3}} \right)$          … (i)

It is given that,

Diameter of the cone $=8cm$

Now, the radius of the cone $=4cm$

Assume the height of the cone be x cm

Volume of the cone $1/3\pi \times {{4}^{2}}\times h$        ….. (ii)

As the volume of the hollow sphere and cone are equal. We can equate equations (i) and (ii)

Then, we get

$4/3\pi \times \left( {{4}^{3}}-{{2}^{3}} \right)=1/3\pi \times {{4}^{2}}\times h$

$4\times \left( 64-8 \right)=16\times h$

$h=14$

Therefore, the height of the cone so obtained will have a height of $14cm$