Answer:
The height of this cone is
[tex]\displaystyle \frac{25}{4}[/tex],
which is the same as 6.25 in decimals.
Step-by-step explanation:
Consider the formula for the volume [tex]V[/tex] of a cone:
[tex]\displaystyle V = \frac{1}{3} \pi\cdot r^{2}\cdot h[/tex],
where
- [tex]r[/tex] is the radius of the base of the cone, and
- [tex]h[/tex] is the height of the cone.
For this cone,
- [tex]V = 300\;\pi[/tex],
- [tex]r = 12[/tex], and
- [tex]h[/tex] is to be found.
Rearrange the equation to find the height of this cone.
[tex]\displaystyle V = \frac{1}{3} \pi\cdot r^{2}\cdot h[/tex],
[tex]3\;V = \pi \cdot r^{2}\cdot h[/tex],
[tex]\displaystyle \frac{3\;V}{\pi\cdot r^{2}} = h[/tex].
Therefore,
[tex]h = \displaystyle \frac{3\;V}{\pi\cdot r^{2}} = \frac{3\times 300\;\pi}{{12}^{2}\; \pi} = \frac{25}{4} = 6.25[/tex].
