## Precalculus (6th Edition) Blitzer

If a cylindrical soft drink has a volume of $12$ fluid ounces, approximately $22\text{ cubic}\text{ }\text{inches}$, then the surface area of the can, $A$ in square inches as a function of its radius $r$ is given as: $A\left( r \right)=2\pi {{r}^{2}}+\frac{44}{r}$.
We have a cylindrical can. The volume of the can is: $\text{V=}\pi {{r}^{2}}h$ And the volume is $22\text{~cubic}\text{ }\text{inches}$ Therefore, \begin{align} & \text{22=}\pi {{r}^{2}}h \\ & h=\frac{22}{\pi {{r}^{2}}} \end{align} The area of the can: $A=2\pi {{r}^{2}}+2\pi rh$ Now put the value of $h$ in the above equation, \begin{align} & A=2\pi {{r}^{2}}+2\pi rh \\ & =2\pi {{r}^{2}}+2\pi r\left( \frac{22}{\pi {{r}^{2}}} \right) \\ & =2\pi {{r}^{2}}+\frac{44}{r} \end{align} Here, $A$ is the function of $r$ (can radius), Hence $A$ is expressed as, $A\left( r \right)=2\pi {{r}^{2}}+\frac{44}{r}$