A spherical shell with internal radius r is converted into a solid sphere whose volume is equal to its cavity - Maths - Surface Areas and Volumes

Question

A spherical shell with internal radius r is converted into a solid
sphere whose volume is equal to its cavity Find the thickness of
the shell

Muskaan Talwar · Accepted Answer

Dear Student,

Let R be the external radius
Volume of sphere=Volume of shellVolume of cavity=Volume of shell43πr3=43πR3-r3⇒r3=R3-r3⇒2r3=R3⇒R=213rNow thickness of shell=R-r=213r-r=213-1r

Regards

A spherical shell with internal radius r is converted into a solid sphere whose volume is equal to its cavity. Find the thickness of the shell.