Q 1 :    

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm, the ice-cream melts at the rate of 81 ${\mathrm{cm}}^3$/min and the thickness of the ice-cream layer decreases at the rate of $\frac{1}{4\mathrm{\pi }}$ cm/min. The surface area (in ${\mathrm{cm}}^2$) of the chocolate ball (without the ice-cream layer) is:          [2025]

• 128$\mathrm{\pi }$

   

• 225$\mathrm{\pi }$

   

• 196$\mathrm{\pi }$

   

• 256$\mathrm{\pi }$