To find the volume of a sphere with a radius of 24 centimeters, we use the formula for the volume of a sphere, which is:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
Here, [tex]\( r \)[/tex] is the radius of the sphere. Given that the radius [tex]\( r \)[/tex] is 24 centimeters, we plug this value into the formula:
[tex]\[
V = \frac{4}{3} \pi (24)^3
\][/tex]
We need to compute [tex]\( 24^3 \)[/tex]:
[tex]\[
24^3 = 24 \times 24 \times 24 = 13824
\][/tex]
Next, we multiply this result by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[
\frac{4}{3} \times 13824 = 18432
\][/tex]
Therefore, the volume of the sphere is:
[tex]\[
V = 18432 \pi \, \text{cm}^3
\][/tex]
So, the correct answer to fill in the blank is:
[tex]\[
V = 18432 \pi \, \text{cm}^3
\][/tex]
