To find the volume of a sphere given its diameter, follow these steps:
1. Determine the Radius: The diameter of the sphere is given as [tex]\( 14 \)[/tex] feet. The radius of a sphere is half its diameter. Hence,
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \, \text{feet}
\][/tex]
2. Write the Formula for the Volume of a Sphere: The formula to find the volume [tex]\( V \)[/tex] of a sphere is:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
3. Substitute the Radius into the Volume Formula: Now, substitute the value of the radius [tex]\( r = 7 \)[/tex] feet into the formula:
[tex]\[
V = \frac{4}{3} \pi (7)^3
\][/tex]
4. Calculate [tex]\( 7^3 \)[/tex]: First, find the cube of the radius:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
5. Plug the Cubed Radius Back into the Volume Formula:
[tex]\[
V = \frac{4}{3} \pi (343)
\][/tex]
6. Simplified Equation: This gives us the equation for the volume of the sphere:
[tex]\[
V = \frac{4}{3} \pi (7)^3
\][/tex]
Therefore, the correct equation that finds the volume of the sphere is:
[tex]\[
\boxed{V = \frac{4}{3} \pi (7)^3}
\][/tex]
