To find the volume of a right circular cone, we'll use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\(\pi\)[/tex] is a mathematical constant approximately equal to 3.14159, [tex]\(r\)[/tex] is the radius of the cone's base, and [tex]\(h\)[/tex] is the cone's height.
For our specific problem, we have:
- The diameter of the cone's base, [tex]\( d = 14.4 \)[/tex] feet. Since the radius is half of the diameter, the radius [tex]\( r \)[/tex] will be [tex]\( \frac{d}{2} = \frac{14.4}{2} = 7.2 \)[/tex] feet.
- The height of the cone, [tex]\( h = 2.7 \)[/tex] feet.
Now, let's substitute the radius and height into the formula for the volume of the cone:
[tex]\[ V = \frac{1}{3} \pi (7.2)^2 (2.7) \][/tex]
We square the radius:
[tex]\[ V = \frac{1}{3} \pi (51.84) (2.7) \][/tex]
Now, let's multiply [tex]\(51.84\)[/tex] by [tex]\(2.7\)[/tex]:
[tex]\[ V = \frac{1}{3} \pi (139.968) \][/tex]
Next, we can calculate [tex]\( \frac{1}{3} \)[/tex] of [tex]\(139.968\)[/tex]:
[tex]\[ V = \pi (46.656) \][/tex]
Lastly, it's time to multiply by [tex]\(\pi\)[/tex]:
[tex]\[ V = 146.6 \][/tex] cubic feet (with [tex]\(\pi\)[/tex] approximated to its actual value in the final calculation).
So, the volume of the cone is [tex]\(146.6\)[/tex] cubic feet rounded to the nearest tenth of a cubic foot.
