Sure, let's break down the solution step-by-step.
1. Identify the Given Values:
- Height ([tex]\( h \)[/tex]) of the cone = 10.6 meters
- Diameter ([tex]\( d \)[/tex]) of the base of the cone = 18.5 meters
2. Calculate the Radius of the Base:
The radius ([tex]\( r \)[/tex]) is half of the diameter.
[tex]\[
r = \frac{d}{2} = \frac{18.5}{2} = 9.25 \text{ meters}
\][/tex]
3. Formula for the Volume of a Right Circular Cone:
The formula to find the volume ([tex]\( V \)[/tex]) of a right circular cone is:
[tex]\[
V = \frac{1}{3} \pi r^2 h
\][/tex]
4. Plug in the Known Values into the Formula:
[tex]\[
V = \frac{1}{3} \pi (9.25)^2 (10.6)
\][/tex]
- First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[
r^2 = 9.25^2 = 85.5625
\][/tex]
- Now, multiply by the height ([tex]\( h \)[/tex]):
[tex]\[
85.5625 \times 10.6 = 906.9625
\][/tex]
- Then, multiply by [tex]\( \frac{1}{3} \pi \)[/tex]:
[tex]\[
V = \frac{1}{3} \pi \times 906.9625
\][/tex]
5. Compute the Volume:
Using the value of [tex]\( \pi \approx 3.141592653589793 \)[/tex],
[tex]\[
V \approx \frac{1}{3} \times 3.141592653589793 \times 906.9625 \approx 949.7689090271442
\][/tex]
6. Round the Volume to the Nearest Tenth:
The computed volume is 949.7689090271442 cubic meters. When rounding to the nearest tenth, the result is:
[tex]\[
V \approx 949.8 \text{ cubic meters}
\][/tex]
Therefore, the volume of the right circular cone, rounded to the nearest tenth, is [tex]\( 949.8 \)[/tex] cubic meters.
