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) = (175)/(7 \pi )`

`r^(2) = (25)/( \pi )`

`r= \sqrt{ (25)/( \pi ) }`

`r= (5)/( √( \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= (5)/( √( \pi ) )` and
`h=7`, so lets replace those values in our area formula:

`A=2 \pi ( (5)/( √( \pi ) ) )(7)+2 \pi ( (5)/( √( \pi ) ))^(2)`

`A= (70 \pi )/( √( \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.