Answer
$x=4.5$
$\text{Surface area}\approx183\,ft^{2}$
$\text{Volume}\approx183\,ft^{3}$
Work Step by Step
$\text{Surface area}=2\pi r^{2}+2\pi rh$
$\text{Volume}=\pi r^{2}h$
Here, $r$ is the radius and $h$ is the height of the cylinder.
Given: $\text{Surface area}=\text{Volume}$ $\implies 2\pi r^{2}+2\pi r h=\pi r^{2}h$
Dividing both sides of the above equation by $\pi r$, we get
$2r+2h=rh$
$\text{Diameter } 2r=7\frac{1}{5}\,ft=\frac{36}{5}\,ft$
$r=\frac{1}{2}\times\frac{36}{5}\,ft=3.6\,ft$
$h=x\,ft$
Substituting these values, we have $\frac{36}{5}+2x=3.6x$
$\implies \frac{36}{5}=3.6x-2x=1.6\,x$
$\implies x=\frac{36}{5\times1.6}=4.5$
$\text{Surface area}=2\pi(3.6)^{2}+2\pi(3.6)(4.5)$
$\approx183\,ft^{2}$
$\text{Volume}=\pi(3.6)^{2}(4.5)\approx183\,ft^{3}$
