To calculate the lateral area, we must know that the lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder.
Note that the base is congruent to the top face. Therefore, their circumferences are the same.
\begin{gathered}
L=\pi dh
\end{gathered}
In this formula, $d$ is the diameter of the base and $h$ is the height of the cylinder. In the given diagram, we can see that the diameter $\col{d}$ is equal to $\col{14}$ feet and that the height $\colII{h}$ is equal to $\colII{32.5}$ feet. If we substitute these values in the formula, we can obtain the lateral area of the given cylinder.
The lateral area of the cylinder is about $1429.4\text{ ft}^2.$
Surface area
To calculate the surface area of a cylinder, we can use the following formula.
\begin{aligned}
S=L+2\pi r^2
\end{aligned}
In this formula, $L$ is the lateral area of the cylinder and $r$ is the radius of the base. Let's first calculate the value of $r,$ given that diameter $\col{d}$ is equal to $\col{14}\text{ ft}$ and that $r=\frac{d}{2}.$
\begin{aligned}
r=\dfrac{\col{14}}{2} \, &\Leftrightarrow \, r=\colIV{7}
\end{aligned}
Now, we can substitute $\colV{L}$ with $\colV{1429.4}$ and $\colIV{r}$ with $\colIV{7}$ into the formula for $S.$ Let's do it!
