The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.

Given,

Internal diameter of the hemisphere = 6 cm

External diameter of the hemisphere = 10 cm

Diameter of cone = 14 cm

So we have,

Internal radius(r) of the hemisphere = 3 cm

External radius(R) of the hemisphere = 5 cm

Radius of cone = 7 cm

Now,

Volume of the hollow hemisphere = Volume of the cone
Volume of the hollow hemisphere =

Volume of the cone =

So,

= 2 × 98 = 49 × h

= h

So,

h = = 4 cm

Thus, the height of the cone formed is 4 cm.