• question_answer The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint $1\text{ }c{{m}^{2}}$of the surface is$Rs.\text{ }0.05$.Find the total cost to painting the vessel all over.    A)  Rs.108.32                  B)  Rs.296.28                  C)  Rs.101.59                  D)  Rs. 96.28

External radius of hemispherical vessel ${{r}_{1}}=\frac{25}{2}\,cm$ External curved surface area of hemispherical; vessel $=2\pi \,\,{{r}_{1}}^{2}=2\times \frac{22}{7}\times {{\left( \frac{25}{2} \right)}^{2}}=\frac{6875}{7}\,c{{m}^{2}}$ Internal curved surface area of hemispherical vessel $=2\pi {{r}_{2}}^{2}$ $=2\times \frac{22}{7}\times {{12}^{2}}=\frac{6336}{7}c{{m}^{2}}$ Area of top of the hemispherical vessel        $=\pi {{r}_{1}}^{2}-\pi {{r}_{2}}^{2}=\pi \left[ {{\left( \frac{25}{2} \right)}^{2}}-{{12}^{2}} \right]$ $=\frac{22}{7}\left[ \frac{625-567}{4} \right]=\frac{22}{7}\times \frac{49}{4}=38.5c{{m}^{2}}$ Total surface area of the vessel         $=\frac{6875}{7}+\frac{6336}{7}+38.5=1925.78\,c{{m}^{2}}$ Cost of painting the vessel at the rate of $Rs.0.05\text{ }per\text{ }c{{m}^{2}}=1925.78\times 0.05=Rs.96.28~$