A hollow sphere of external and internal diameter 8 cm and 4 cm respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone.
External diameter of hollow sphere = D = 8 cm
⇒ External radius of hollow sphere = R = D/2
⇒ R = 8/2
⇒ R = 4 cm
Internal diameter of hollow sphere = d = 4 cm
⇒ Internal radius of hollow sphere = r = d/2
⇒ r = 4/2
⇒ r = 2 cm
Let the height of the resulting cone be ‘h’ cm
Let the volume of External sphere be V1 and that of internal be V2.
Explanation: Here the volume of hollow sphere will be equal to the volume of the resulting cone as the resulting cone is formed by melting the sphere.
Volume of the External sphere=
(put the value of R)
Volume of sphere = V = External volume – Internal volume
Given base radius of the resulting cone = r’ = 8 cm
Le the height be ‘h’ and volume of the resulting cone be V’
(putting value of r' )
Equate equation 3 and 4,
⇒ V = V’
⇒ 224 = 64h
⇒ h = 224/64
∴ h = 3.5 cm
The height of resulting cone is 3.5 cm.