Respuesta :

mbh292
The volume of a cone is:
[tex]v = \frac{\pi {r}^{2} h }{3} [/tex]
Plug in the values (I am assuming not 1/18π but 1/18×π):
[tex] \frac{1}{18} \pi = \frac{\pi { \frac{1}{3} }^{2} h}{3} [/tex]
Get rid of the radius:
[tex] { \frac{1}{3} }^{2} = \frac{1}{9} [/tex]
Continue:
[tex] \frac{\pi}{18} = \frac{\pi h}{3} \times \frac{1}{9} = \frac{\pi h}{18} [/tex]
Remove the denominators:
[tex]\pi = \pi h[/tex]
Divide both sides by π :
[tex]h = 1[/tex]

The volume of the cone is the space that is occupied by the cone. The height of the cone is [tex]\dfrac{3}{2\pi^2}[/tex].

What is the volume of the cone?

The volume of the cone is the space that is occupied by the cone. It is calculated with the formula,

[tex]\text{Volume of the cone} = \dfrac{1}{3}\pi r^2h[/tex]

The radius of the cone is the ratio of diameter and 2,

[tex]\text{Radius of the cone}=\dfrac{\text{Diameter of the cone}}{2} = \dfrac{\frac{2}{3}}{2}=\dfrac{1}{3}[/tex]

We know that the volume of the cone is given by the formula,

[tex]\text{Volume of the cone} = \dfrac{1}{3}\pi r^2h[/tex]

We know the volume of the cone and the radius of the cone, therefore,

[tex]\dfrac{1}{18\pi} = \dfrac{1}{3}\pi \times (\dfrac{1}{3})^2\times h\\\\\dfrac{1}{18\pi} = \dfrac{1}{3}\pi \times (\dfrac{1}{9})\times h\\\\\dfrac{3 \times 9}{18\pi^2} = h\\\\h = \dfrac{3}{2\pi^2}[/tex]

Hence, the height of the cone is [tex]\dfrac{3}{2\pi^2}[/tex].

Learn more about Volume of the cone:

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