To find the volume of a right circular cone with given dimensions, we will use the volume formula for a cone, which is:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius of the base,
- [tex]\( h \)[/tex] is the height,
- [tex]\( \pi \)[/tex] is a constant (approximately 3.14159).
Let's break down the steps:
1. Identify the given values:
- Height ([tex]\( h \)[/tex]) = 18.5 inches
- Diameter of the base = 17.5 inches
2. Calculate the radius:
[tex]\[
r = \frac{\text{Diameter}}{2} = \frac{17.5}{2} = 8.75 \text{ inches}
\][/tex]
3. Substitute the known values into the volume formula:
[tex]\[
V = \frac{1}{3} \pi (8.75)^2 (18.5)
\][/tex]
4. Evaluate the square of the radius:
[tex]\[
8.75^2 = 76.5625
\][/tex]
5. Perform the multiplication inside the formula:
[tex]\[
V = \frac{1}{3} \pi (76.5625) (18.5)
\][/tex]
6. Multiply these numbers to find the volume:
[tex]\[
V = \frac{1}{3} \pi \times 1416.41625
\][/tex]
7. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[
V \approx \frac{1}{3} \times 3.14159 \times 1416.41625 \approx 1483.257156499556
\][/tex]
8. Round the volume to the nearest tenth:
[tex]\[
V \approx 1483.3 \text{ cubic inches}
\][/tex]
Hence, the volume of the right circular cone, rounded to the nearest tenth of a cubic inch, is approximately [tex]\( 1483.3 \)[/tex] cubic inches.
