How do you find the radius and height of a cylinder if you are given the area ?

Question

anonymous · Answer

You would have to be given the area AND the height to get the radius.

You would have to be given the area AND the radius to get the height.

anonymous · Answer

A is area, r is radius, h is height

A = pi*r^2*h........solve for the variable you want to find and plug in for the variables you know.

whpalmer4 · Answer

@bangkokgarrett
What you've given is the formula for the volume (though you've labeled it area).

The surface area of a cylinder with radius $r$ and height $h$ is the area of the two ends (which are circles), plus the area of the side (which is a rectangle).  The ends have area $A_{end} = \pi r^2$ and there are two of them, so the contribution to the area is $A_{ends} = 2\pi r^2$

The side of the cylinder is just a rectangle with height $h$ and length $2\pi r$ (which is the circumference).  Therefore, $A_{side} = 2\pi r h$

The total surface area of the cylinder is thus
$$A_{cyl} = 2\pi r h + 2\pi r^2$$
If you're calculating, $$A_{cyl} = 2\pi r(h+r)$$might be slightly more convenient.

But in any case, yes, you need to have some means to determine the relationship between radius and height (such as knowing one of them, or a ratio, or also knowing volume) in order to be able to find values for both.