Given, 

internal radius of hollow sphere, r = (\(\frac{4}2\)) = 2 cm 

External radius = \(\frac{8}2\) = 4 cm 

Volume of hollow sphere = \(\frac{4}{3}π(R^3 - r^3)\)

= \(\frac{4}{3}π(4^3 - 2^3)\) --------(i) 

Given, 

diameter of the cone = 8 cm 

∴ Radius of the cone = 4 cm 

Let height of the cone be h 

Volume of the cone = \(\frac{1}{3}πr^2h{}\)

= \(\frac{1}{3}π4^2h{}\)--------(ii) 

Since hollow sphere is melted into a cone so their volumes are equal,

\(\frac{4}{3}\) π × (4³ – 2³) = \(\frac{1}{3}\) π × 4² × h

4 x (64 – 8) = 16 x h

4 x 56 = 16 x h

h = \(\frac{4 \times 56}{16}\)

∴ h = 14 cm

Let the height of the cone be h cm.
Let the height of the cone be h cm.
Volume of the cone = ⅓ πr1²h
= ⅓ π × 4² × h = 16πh/3

Volume of the cone = Volume of the hollow sphere
16πh/3 = 4/3π(56)
16h = 4 ×56
h = (4 × 56)/16
h = 56/4 = 14 cm

Hence, the height of the cone is 14 cm.

= ⅓ π × 4² × h = 16πh/3

Volume of the cone = Volume of the hollow sphere
16πh/3 = 4/3π(56)
16h = 4 ×56
h = (4 × 56)/16
h = 56/4 = 14 cm

Hence, the height of the cone is 14 cm.