Answer:
[tex]\boxed {\boxed {\sf 60 \pi , 188.4, \ or \ 188.495559 \ m^3}}[/tex]
Step-by-step explanation:
The formula for the volume of a cone is:
[tex]v=\frac{1}{3} \pi r^2h[/tex]
First, we must find the radius. The diameter is 12 meters and the radius is half of the diameter.
The radius is 6 meters and the height is 5 meters.
[tex]v=\frac{1}{3} \pi (6 \ m)^2 (5 \ m )[/tex]
Solve the exponent.
- (6 m)²= 6 m * 6 m = 36 m²
[tex]v=\frac{1}{3} \pi (36 \ m^2) (5 \ m )[/tex]
Multiply the numbers in parentheses.
[tex]v=\frac{1}{3} \pi (180 \ m^2)[/tex]
Multiply by 1/3 or divide by 3.
[tex]v= 60 \pi \ m^3[/tex]
There are 3 ways to finish solving this.
1. In Terms of Pi
Leave the answer as it is, with pi included: [tex]v= 60 \pi \ m^3[/tex]
2. Using 3.14 as Pi
[tex]v= 60 (3.14) \ m^3 =188.4 \ m^3[/tex]
3. Using the Pi Button on a calculator
[tex]v=60 (3.14159265) \ m^3=188.495559 \ m^3[/tex]
The volume of the cone is 60π, 188.4, or 188.495559 cubic meters.
