Sure, let's go through the process step by step to find the volume of a sphere with a radius of 5 inches.
We are given the formula for the volume [tex]\( V \)[/tex] of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
1. Substitute the given radius into the formula:
[tex]\[
V = \frac{4}{3} \pi (5^3)
\][/tex]
[tex]\[
V = \frac{4}{3} \pi (125)
\][/tex]
2. Evaluate the power:
Since [tex]\( 5^3 = 5 \times 5 \times 5 = 125 \)[/tex], we then have:
[tex]\[
V = \frac{4}{3} \pi (125)
\][/tex]
3. Simplify:
To continue simplifying:
[tex]\[
V = \frac{4}{3} \pi \times 125
\][/tex]
[tex]\[
V = \frac{500}{3} \pi
\][/tex]
So the volume is:
[tex]\[
V \approx 523.5987755982989 \, \text{in}^3
\][/tex]
Therefore, the volume of a sphere with a radius of 5 inches is approximately [tex]\( 523.5987755982989 \)[/tex] cubic inches.
