Question

Find the volume of a right circular cone that has a height of 14.7 ft and a base with a circumference of 13 ft. Round your answer to the nearest tenth of a cubic foot.

Answer 1

Answer:

$C= 2\pi r$

$r = \frac{C}{2\pi} =\frac{13 ft}{2\pi}= 2.069 ft$

$V =\frac{\pi (2.069 ft)^2 *14.7 ft}{3}= 65.89 ft^3 \approx 65.9 ft^3$

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:

$V = \frac{\pi r^2 h}{3}$

Where:

$r$ represent the radius

$h = 14.7$ represent the heigth

We know the length of the circumference on this case $C = 13 ft$ and by properties we know that:

$C= 2\pi r$

Solving for r we got:

$r = \frac{C}{2\pi} =\frac{13 ft}{2\pi}= 2.069 ft$

Now replacing the value of the radius and heigth into the formula for the volume we got:

$V =\frac{\pi (2.069 ft)^2 *14.7 ft}{3}= 65.89 ft^3 \approx 65.9 ft^3$

So then the final answer after round to the nearest tenth is 65.9 ft^3