Question

The volume of an oblique cone with equal diameter and height is 18\pi cm^3. find the height and radius.

Answer 1

The formula of a volume of a cone:

$V=\dfrac{1}{3}\pi r^2h$

We have:

$2r=x\to r=\dfrac{x}{2}\\\\h=x\\\\V=18\pi\ cm^3$

substitute:

$\dfrac{1}{3}\pi\left(\dfrac{x}{2}\right)^2\cdot x=18\pi\ \ \ \ |:\pi\\\\\dfrac{1}{3}\cdot\dfrac{x^2}{4}\cdot x=18\\\\\dfrac{x^3}{12}=18\ \ \ \ |\cdot12\\\\x^3=216\to x=\sqrt[3]{216}\\\\x=6\ cm$

$h=x\to h=6\ cm\\\\r=\dfrac{x}{2}\to r=\dfrac{6}{2}=3\ cm$

Answer:

height = 6 cm

radius = 3 cm