Question

A cylinder's volume can be calculated by the formula V = Bh , where V represents the volume, B stands for the base area, and h stands for the height. The volume of a cylinder can be modeled by 12(pie)x^5 - 20(pi)x^4 +6(pi)x^3 cubic units. If the base area is 2(pi)x^2 square units, find the cylinder's height.

Answer 1

`\begin{gathered} V=Bh \\ h=(V)/(B) \\ V=\text{ }12\pi x^5-20\pi x^4+6\pi x^3 \\ B=2\pi x^2 \\ h=\frac{\text{ }12\pi x^5-20\pi x^4+6\pi x^3}{2\pi x^2} \\ h=\frac{(2\pi x^2)\cdot\text{ (6}x^3-10x^2+3x)}{2\pi x^2} \\ h=\text{6}x^3-10x^2+3x \\ cylinder^(\prime)sheight\text{ is 6}x^3-10x^2+3x \end{gathered}`