Question

Find the area of A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is

Answer 1

To find the area of the cylinder we need to find its volume first. Remember that the formula for the volume of a cylinder is $V= \pi r^{2} h$
where:
$V$ is the volume 
$r$ is the radius 
$h$ is the height 
From the question we know that $A=175$ and $h=7$. Lets replace those values in our volume formula:
$175= \pi r^{2} 7$
Now we can solve for $r$ to find our radius:
$r^{2} = \frac{175}{7 \pi }$
$r^{2} = \frac{25}{ \pi }$
$r= \sqrt{ \frac{25}{ \pi } }$
$r= \frac{5}{ \sqrt{ \pi } }$

Now that we know the radius, we can use the formula for the area of a cylinder $A=2 \pi rh+2 \pi r^{2}$
where:
$A$ is the area
$r$ is the radius 
$h$ is the height
We know now that $r= \frac{5}{ \sqrt{ \pi } }$ and $h=7$, so lets replace those values in our area formula:
$A=2 \pi ( \frac{5}{ \sqrt{ \pi } } )(7)+2 \pi ( \frac{5}{ \sqrt{ \pi } })^{2}$
$A= \frac{70 \pi }{ \sqrt{ \pi } } +50$
$A=174.07$

We can conclude that the area of a cylinder that has a volume of 175 cubic units and a height of 7 units is 174.07 square units.