Find the volume of a right circular cone that has a height of 5.3 fr and a base with a circumference of 19.1 ft. Round your answer to the nearest tenth of a cubic foot.

Question

asked Jun 11, 2021 75.3k views

2 Answers

Pardahlman · Answer 1 · 2021-06-17T19:55:33+0000

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

We must find the radius knowing that the circumference of the base of the cone is
$19.1 \ ft$

$2 \pi * r = 19.1\\r = \frac {19.1} {2 \pi}\\r = 3.04 \ ft$

Thus, we substitute in the formula:

$V = \frac {1} {3} * \pi * (3.04) ^ 2 * 5.3\\V = \frac {1} {3} * \pi * 9.25 * 5.3\\V = \frac {1} {3} * 154.0165\\V = 51.34$

Thus, the volume of the cone is:
$51.34 \ ft ^ 3$

Answer:

$51.3 \ ft ^ 3$