Question

find the volume of a right circular cone that has a height of 3.9 ft and a base with a radius of 14.7 ft. round your answer to the nearest tenth of a cubic foot.

Explanation:

Step1: Recall the formula for the volume of a cone

The volume \( V \) of a right circular cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Substitute the given values into the formula

We are given that \( r = 14.7\) ft and \( h=3.9\) ft. Substituting these values into the formula, we get:

$$ V=\frac{1}{3}\times\pi\times(14.7)^{2}\times3.9 $$

First, calculate \( (14.7)^{2}=14.7\times14.7 = 216.09 \)
Then, multiply \( 216.09\times3.9=842.751 \)
Next, multiply \( \frac{1}{3}\times842.751 = 280.917 \)
Now, multiply by \( \pi \) (using \( \pi\approx3.14159 \)): \( V\approx280.917\times3.14159 \)

$$ V\approx280.917\times3.14159\approx882.7 $$

(rounded to the nearest tenth)

Answer:

The volume of the right circular cone is approximately \( 882.7 \) cubic feet.