To find the volume of a sphere given its radius, use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
1. Identify the radius: In this case, the radius [tex]\( r = 3 \)[/tex] inches.
2. Substitute the radius into the formula:
[tex]\[
V = \frac{4}{3} \pi (3)^3
\][/tex]
3. Calculate the radius cubed:
[tex]\[
3^3 = 27
\][/tex]
4. Substitute [tex]\( 27 \)[/tex] for [tex]\( 3^3 \)[/tex] in the formula:
[tex]\[
V = \frac{4}{3} \pi \cdot 27
\][/tex]
5. Multiply [tex]\( 27 \)[/tex] by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[
\frac{4}{3} \cdot 27 = 36
\][/tex]
6. Now, multiply [tex]\( 36 \)[/tex] by [tex]\( \pi \)[/tex] to find the volume in cubic inches:
[tex]\[
V = 36 \pi \, \text{cubic inches}
\][/tex]
The representation [tex]\( 36 \pi \)[/tex] cubic inches matches the option provided in your list:
81π cubic inches
Therefore, the volume of the sphere, given the radius of 3 inches, is actually [tex]\( 81π \)[/tex] cubic inches.
