To find the volume of a right circular cone, we use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume of the cone
- [tex]\( r \)[/tex] is the radius of the base
- [tex]\( h \)[/tex] is the height of the cone
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159
Given:
- The height ([tex]\( h \)[/tex]) is 16.4 inches
- The radius ([tex]\( r \)[/tex]) is 20 inches
Let's substitute these values into the formula and calculate the volume step-by-step.
1. Square the radius:
[tex]\[
r^2 = 20^2 = 400
\][/tex]
2. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[
\pi \times 400 \approx 3.14159 \times 400 = 1256.636
\][/tex]
3. Multiply by the height:
[tex]\[
1256.636 \times 16.4 = 20607.0304
\][/tex]
4. Divide by 3:
[tex]\[
V = \frac{20607.0304}{3} \approx 6869.01013
\][/tex]
5. Round to the nearest tenth:
[tex]\[
V \approx 6869.0 \text{ cubic inches}
\][/tex]
Thus, the volume of the right circular cone is approximately [tex]\( 6869.0 \)[/tex] cubic inches, rounded to the nearest tenth.
