Question

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

Answer 1

Given

Internal diameter of hollow sphere (r) = 4cm 

So, the internal radius of hollow sphere = 2 cm

External diameter (R) = 8cm

So, the external radius of hollow sphere = 4 cm

Volumeof hollow sphere = `4/3pi(R^2-r^2)`

`=4/3pi(4^2 - 2^2)`         ...(1)

Given diameter of cone = 8cm 

Radius of cone = 4cm

Let height of cone be x cm

Volume of cone `=1/3pir^2h`

`=1/3pixx(4)^2h`          ...(2)

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

(1) = (2)

⇒ `4/3 pi xx (4^3 - 2^3) = 1/3 pi xx 4^2 xx h`

⇒ `4 xx (64 - 8) = 16 xx h`

⇒ h = 14

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