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..


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