From a solid cylindrical wooden block of height 18 cm and radius 7.5 cm, a conical cavity of the same height and same radius is taken out. What is total surface area (in cm²) of the remaining solid?

Solution (By Examveda Team)

$$\eqalign{ & {l^2} = {r^2} + {h^2} \cr & {l^2} = {\left( {7.5} \right)^2} + {\left( {18} \right)^2} \cr & {l^2} = \frac{{225}}{4} + 324 \cr & {l^2} = \frac{{1521}}{4} \cr & l = \frac{{39}}{2} \cr & {\text{Total surface area}} = \pi rl + 2\pi rh + \pi {r^2} \cr & = \pi r\left[ {l + 2h + r} \right] \cr & = \pi \times \frac{{15}}{2}\left[ {\frac{{39}}{2} + 36 + \frac{{15}}{2}} \right] \cr & = \pi \times \frac{{15}}{2}\left[ {\frac{{126 \times 15}}{2}} \right] \cr & = \left[ {\frac{{945}}{2}} \right]\pi \cr & = 472.5\pi \cr} $$