A spherical metallic shell with 6 cm external radius weight 6688 g. What is the thickness of the shell if the density of metal is 10.5 g per cm³?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Volume of Metallic shell}} \cr & = V = \frac{4}{3}\pi \left( {{R^3} - {r^3}} \right) \cr & {\text{Total weight of Metallic shell}} \cr & \Rightarrow 10.5 \times V = 6688 \cr & \Rightarrow 10.5 \times \frac{4}{3} \times \frac{{22}}{7}\left( {{6^3} - {r^3}} \right) = 6688 \cr & \Rightarrow r = 4 \cr & {\text{Thickness}} = 6 - 4 = 2 \cr} $$