Question

The volume of the right cone below is 36π units ^3. Find the value of x

Answer 1

Step-by-step explanation

The formula to find the volume of a cone is:

`\begin{gathered} V=(1)/(3)\pi r{}{}^2h \\ \text{ Where} \\ V\text{ is the volume} \\ r\text{ is the radius} \\ h\text{ is the heigth} \end{gathered}`

Then, we replace the know values in the above formula and solve for h.

`\begin{gathered} V=36\pi \\ r=\frac{\text{ diameter}}{2}=(6)/(2)=3 \\ h=x \end{gathered}`
`\begin{gathered} V=(1)/(3)\pi r^2h \\ 36\pi=(1)/(3)\pi(3)^2x \\ 36\pi=(9\pi x)/(3) \\ 36\pi=3\pi x \\ \text{ Divide by }3\pi\text{ from both sides} \\ (36\pi)/(3\pi)=(3\pi x)/(3\pi) \\ 12=x \end{gathered}`Answer

The value of x is 12 units.