To find the volume of a right circular cone with a height of 13.8 meters and a base circumference of 15.8 meters, we'll go through a few steps:
Step 1: Determine the radius of the base of the cone.
The formula for the circumference ([tex]\( C \)[/tex]) of a circle is:
[tex]\[ C = 2\pi r \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle, and [tex]\( \pi \)[/tex] is approximately [tex]\( 3.14159 \)[/tex].
Given the circumference of the base is 15.8 meters, we can solve for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{C}{2\pi} \][/tex]
[tex]\[ r = \frac{15.8}{2\pi} \][/tex]
[tex]\[ r \approx 2.5146481008519466 \text{ meters} \][/tex]
Step 2: Calculate the volume of the cone.
The formula for the volume ([tex]\( V \)[/tex]) of a cone is:
[tex]\[ V = \frac{1}{3}\pi r^2 h \][/tex]
where [tex]\( h \)[/tex] is the height of the cone.
Plugging the values we have:
[tex]\[ V = \frac{1}{3}\pi (2.5146481008519466)^2 \times 13.8 \][/tex]
[tex]\[ V \approx 91.38231198495974 \text{ cubic meters} \][/tex]
Step 3: Round the volume to the nearest tenth.
The volume to the nearest tenth of a cubic meter is approximately [tex]\( 91.4 \)[/tex] cubic meters.
So the volume of the right circular cone with a height of 13.8 meters and a base circumference of 15.8 meters, rounded to the nearest tenth, is [tex]\( 91.4 \)[/tex] cubic meters.
