Question

Find the height of a cone shaped room with a diameter of 144 ft and a volume of 81430.1 cubic ft.

Answer 1

For this case we have that by definition, the volume of a cone is given by:

`V = \frac {1} {3} * \pi * r ^ 2 * h`

Where:

r: It is the radius of the cone

h: Is the height of the cone

According to the data of the statement we have to:

`r = \frac {144} {2} = 72 \ ft\\V = 81430.1 \ ft`

Substituting we have:

`81430.1 = \frac {1} {3} * \pi * (72) ^ 2 * h\\81430.1 = \frac {1} {3} * \pi * 5184 * h\\81430.1 = 1728 * \pi * h\\81430.1 = 5425.92 * h\\h = \frac {81430.1} {5425.92}\\h = 15.008`

We have that the height of the cone is approximately
`15 \ ft`

Answer:

`15 \ ft`