To find the volume of a sphere, we use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Here, the radius [tex]\( r \)[/tex] of the sphere is given as 24 centimeters. Substituting [tex]\( r = 24 \)[/tex] into the formula:
[tex]\[ V = \frac{4}{3} \pi (24)^3 \][/tex]
After calculating the value of [tex]\( 24^3 \)[/tex], we multiply by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ V = \frac{4}{3} \pi \times 13824 \][/tex]
[tex]\[ V = \frac{4 \times 13824}{3} \pi \][/tex]
[tex]\[ V = \frac{55296}{3} \pi \][/tex]
[tex]\[ V = 18432 \pi \][/tex]
Thus, the volume of the sphere is:
[tex]\[ V = 18432 \pi \, \text{cm}^3 \][/tex]
Therefore, the correct answer is:
[tex]\[ V = 18432 \pi \, \text{cm}^3 \][/tex]
