Question

Jack knows the surface area of a cylinder and its radius. He wants to find the cylinder's height. He needs to rewrite the formula to find the cylinder's height (h) in terms of the cylinder’s surface area (A) and its radius (r). Which is the correct formula?

Answer 1

If you are only asking for the formula (it's not clear). Here it is. h = V/
`h=V/\pi r2`

Answer 2

For this case, we have that by definition, the surface area of a cylinder, is given by:

`A = 2 \pi * r * h + 2 \pi * r ^ 2`

Where:

A: It is the area of the surface

h: It is the height of the cylinder

r: It's the radio

If you want to find the height as a function of "A", we clear:

Subtracting
`2 \pi * r ^ 2` on both sides of the equation:

`A-2 \pi * r ^ 2 = 2 \pi * r * h`

Dividing both sides of the equation between
`2 \pi * r`:

`\frac {A-2 \pi * r ^ 2} {2 \pi * r} = h`

So, we have "h" as a function of "A"

Answer:

`h = \frac {A-2 \pi * r ^ 2} {2 \pi * r}`