For this case we have that by definition, the volume of a cone is given by:
[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]
Where:
r: It is the radius of the cone
h: Is the height of the cone
We must find the radius knowing that the circumference of the base of the cone is[tex]19.1 \ ft[/tex]
[tex]2 \pi * r = 19.1\\r = \frac {19.1} {2 \pi}\\r = 3.04 \ ft[/tex]
Thus, we substitute in the formula:
[tex]V = \frac {1} {3} * \pi * (3.04) ^ 2 * 5.3\\V = \frac {1} {3} * \pi * 9.25 * 5.3\\V = \frac {1} {3} * 154.0165\\V = 51.34[/tex]
Thus, the volume of the cone is: [tex]51.34 \ ft ^ 3[/tex]
Answer:
[tex]51.3 \ ft ^ 3[/tex]
