If a circle’s area is equal to four times its circumference, what is the diameter?

"The volume of a cylinder is given by the formula V=πr2hV=πr2h, where rr is the radius of the circle on the base of the cylinder and hh is the height of the cylinder.

The formula for circumference is C=2πrC=2πr. We can rearrange this to get a formula for a radius in terms of the circle’s circumference, giving us r=C2πr=C2π.

We also know that the height of the cylinder is four times its circumference, so from this statement, we can derive the formula h=4Ch=4C.

We plug both of these formulas, r=C2πr=C2π and h=4Ch=4C, into their respective positions in the volume formula to get V=π(C2π)2(4C)V=π(C2π)2(4C).

Finally, we simplify.

V=π(C2π)2(4C)V=π(C2π)2(4C)

⟹V=π(C24π2)(4C)⟹V=π(C24π2)(4C)

⟹V=C3π"