To find the volume of a sphere with a radius of [tex]\(\frac{3}{2}\)[/tex] feet, we follow the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( r \)[/tex] is the radius of the sphere,
- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159.
Given the radius [tex]\( r = \frac{3}{2} \)[/tex] feet, we need to calculate:
1. First, calculate [tex]\( r^3 \)[/tex]:
[tex]\[ r^3 = \left(\frac{3}{2}\right)^3 = \frac{3^3}{2^3} = \frac{27}{8} \][/tex]
2. Next, multiply this value by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ \frac{4}{3} \times \frac{27}{8} = \frac{4 \cdot 27}{3 \cdot 8} = \frac{108}{24} = 4.5 \][/tex]
Therefore, the volume of the sphere is:
[tex]\[ V = 4.5 \pi \text{ ft}^3 \][/tex]
So, the volume of the sphere with a radius of [tex]\(\frac{3}{2}\)[/tex] feet is [tex]\( 4.5 \pi \, \text{ft}^3 \)[/tex].
