Question

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

I don't get how to do this

Answer 1

The formula of a volume of a cone:

`V=(1)/(3)\pi r^2h`

We have:

`2r=x\to r=(x)/(2)\\\\h=x\\\\V=18\pi\ cm^3`

substitute:

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

`h=x\to h=6\ cm\\\\r=(x)/(2)\to r=(6)/(2)=3\ cm`

Answer:

height = 6 cm

radius = 3 cm