Answer
$x=10$
$\text{Surface area}\approx196.35\,cm^{2}$
$\text{Volume}\approx196.35\,cm^{3}$
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
$2r+2h=rh$
$r=2.5\,cm$
$h=x\,cm$
Substituting these values, we have
$2(2.5)+2x=2.5x$
$\implies 5+2x=2.5x$
$\implies 5=2.5x-2x=0.5x$
$x=\frac{5}{0.5}=10$
$\text{Surface area}=2\pi(2.5)^{2}+2\pi(2.5)(10)$ $\approx196.35\,cm^{2}$ $\text{Volume}=\pi(2.5)^{2}(10)\approx196.35\,cm^{3}$
