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 $14cm$