College Algebra, Chapter 1, 1.3, Section 1.3, Problem 88

Find the diameters of the cylindrical can if it has a volume of $40 \pi cm^3$ and height of $10 cm$.

Recall that the volume of the cylinder is..


$
\begin{equation}
\begin{aligned}

V =& \pi r^2 h
&& \text{Model}
\\
\\
40 \pi =& \pi r^2 (10)
&& \text{Substitute the given}
\\
\\
\frac{40 \pi}{10 \pi} =& r^2
&& \text{Simplify}
\\
\\
r^2 =& 4
&& \text{Solve for } r
\\
\\
r =& \pm 2
&& \text{Take the square root}
\\
\\
r =& 2 cm
&& \text{Choose } r > 0
\\
\\
d =& \frac{r}{2}
&& \text{Formula for diameter with respect to radius}
\\
\\
d =& \frac{2}{2}
&& \text{Substitute } r
\\
\\
d =& 1 cm
&& \text{Solve for } d

\end{aligned}
\end{equation}
$