Question

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone?

Answer 1

Given,

Internal diameter of hollow sphere = 4 cm

So, the internal radius of hollow sphere = 2 cm

External diameter of hollow sphere = 8 cm

So, the external radius of hollow sphere = 4 cm

We know that,

Volume of the hollow sphere 4/3 π × (4³ – 2³)          … (i)

Also given,

Diameter of the cone = 8 cm

So, the radius of the cone = 4 cm

Let the height of the cone be x cm

Volume of the cone 1/3 π × 4² × h          ….. (ii)

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

So, we get

4/3 π × (4³ – 2³) = 1/3 π × 4² × h

4 x (64 – 8) = 16 x h

h = 14

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