Answer:
[tex] C= 2\pi r[/tex]
[tex] r = \frac{C}{2\pi} =\frac{13 ft}{2\pi}= 2.069 ft[/tex]
[tex] V =\frac{\pi (2.069 ft)^2 *14.7 ft}{3}= 65.89 ft^3 \approx 65.9 ft^3[/tex]
So then the final answer after round to the nearest tenth is 65.9 ft^3
Step-by-step explanation:
For this case we know that the volume for a right ciruclar cone is given by this formula:
[tex] V = \frac{\pi r^2 h}{3}[/tex]
Where:
[tex] r [/tex] represent the radius
[tex] h = 14.7 [/tex] represent the heigth
We know the length of the circumference on this case [tex] C = 13 ft[/tex] and by properties we know that:
[tex] C= 2\pi r[/tex]
Solving for r we got:
[tex] r = \frac{C}{2\pi} =\frac{13 ft}{2\pi}= 2.069 ft[/tex]
Now replacing the value of the radius and heigth into the formula for the volume we got:
[tex] V =\frac{\pi (2.069 ft)^2 *14.7 ft}{3}= 65.89 ft^3 \approx 65.9 ft^3[/tex]
So then the final answer after round to the nearest tenth is 65.9 ft^3
