A cylinder has a volume of 324 cm^3. If the radius of the cylinder is 1 cm more than twice the height, find the dimensions of the cylinder.
I know that formula for the volume of cylinder is $V=\pi r^2 h$, but I do not know what to do next.
2026-03-28 21:26:54.1774733214
Word problem for polynomial equations: Volume of a cylinder given relation between radius and height
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Knowing that volume and height and radius are related by $$V = \pi r^2 h $$ and the restriction from the problem gives $$r = 1 + 2h$$ Also, V = 324. Plugging in these values and multiplying out the r^2 part gives $$ 324 = \pi h (1 + 4h + 4h^2) $$ Rearanging gives $$ 0 = 4h^3 + 4h^2 + h - 324 / \pi $$ A cubic calculator shows that the real answer is about 2.63. www.WolframAlpha.com is a free tool that I like. See picture
The answer is about 2.63066 cm for the height. That implies that the radius is about 6.26132 cm.