Question

A cylinder has a radius of $6\mathrm{inches}$ and a height of $15\mathrm{inches}$. What is the surface area of the cylinder? Express the answer in terms of $\mathrm{\pi }$.

Answer 1

Solve for the surface area of given cylinder:

Given that cylinder has a radius of $6\mathrm{inches}$ and a height of $15\mathrm{inches}$

Surface area of cylinder $\mathrm{SA}=2\mathrm{\pi rh}+2{\mathrm{\pi r}}^2$, where $\mathrm{r}$ is radius and $\mathrm{h}$ is height
$$\begin{gathered} \Rightarrow \mathrm{SA}=2\mathrm{\pi r}(\mathrm{h}+\mathrm{r}) \\ =2\mathrm{\pi }\times 6(15+6) \\ =12\mathrm{\pi }\left(21\right) \\ =252\mathrm{\pi } \\ =252\times 3.14\left[\because \mathrm{\pi }=3.14\right] \\ \Rightarrow \mathrm{SA}=791.28\mathrm{sq}.\mathrm{inches} \end{gathered}$$

Hence, the surface area of cylinder is $791.28\mathrm{sq}.\mathrm{inches}$.