From a solid cylinder of height $\displaystyle 20$ cm and diameter $\displaystyle 12$ cm, a conical cavity of height $\displaystyle 8$ cm and radius $\displaystyle 6$ cm is hallowed out. Find the total surface area of the remaining solid.

Height of cylinder h = $\displaystyle 20$ cm radius of cylinder \(\displaystyle =6 \mathrm{~cm}=\) Radius of cone Height of cone \(\displaystyle =8 \mathrm{~cm}\) Slant height \(\displaystyle l=\sqrt{8^{2}+6^{2}}\) \[=\sqrt{64+36}=10 \mathrm{~cm} \] Surface area of remaining solid = CSA of cylinder + CSA of cone + Area of base of cylinder \(\displaystyle =2 \pi \mathrm{rh}+\pi \mathrm{r} l+\pi \mathrm{r}^{2}=\pi \mathrm{r}[2 \mathrm{~h}+l+\mathrm{r}]\) \(\displaystyle =\frac{22}{7} \times 6[2 \times 20+10+6]=\frac{22}{7} \times 6 \times 56\) \(\displaystyle =1056 \mathrm{~cm}^{2}\)