The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
We have:
[tex]2r=x\to r=\dfrac{x}{2}\\\\h=x\\\\V=18\pi\ cm^3[/tex]
substitute:
[tex] \dfrac{1}{3}\pi\left(\dfrac{x}{2}\right)^2\cdot x=18\pi\ \ \ \ |:\pi\\\\\dfrac{1}{3}\cdot\dfrac{x^2}{4}\cdot x=18\\\\\dfrac{x^3}{12}=18\ \ \ \ |\cdot12\\\\x^3=216\to x=\sqrt[3]{216}\\\\x=6\ cm [/tex]
[tex]h=x\to h=6\ cm\\\\r=\dfrac{x}{2}\to r=\dfrac{6}{2}=3\ cm[/tex]
Answer:
height = 6 cm
radius = 3 cm
