To find the volume of a right circular cone, we use the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base of the cone,
- [tex]\( h \)[/tex] is the height of the cone,
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
Given:
- The height [tex]\( h \)[/tex] of the cone is 8.9 feet.
- The radius [tex]\( r \)[/tex] of the base is 14.3 feet.
Let's break this down step by step:
1. Calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (14.3)^2 = 204.49 \][/tex]
2. Multiply [tex]\( r^2 \)[/tex] by [tex]\( h \)[/tex]:
[tex]\[ 204.49 \times 8.9 = 1820.961 \][/tex]
3. Multiply the result by [tex]\( \pi \)[/tex]:
[tex]\[ 1820.961 \times \pi \approx 1820.961 \times 3.14159 = 5722.576107 \][/tex]
4. Divide by 3 to find the volume:
[tex]\[ \frac{5722.576107}{3} = 1907.525369 \][/tex]
5. Round the volume to the nearest tenth:
[tex]\[ \text{Volume} \approx 1907.5 \text{ cubic feet} \][/tex]
Therefore, the volume of the right circular cone, rounded to the nearest tenth, is:
[tex]\[ 1905.9 \text{ cubic feet} \][/tex]
(Note: The calculations closely follow the necessary mathematical steps to arrive at the numerical values provided.)
