To find the volume [tex]\( V \)[/tex] of a sphere with a given radius [tex]\( r \)[/tex], we use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Given that the radius [tex]\( r \)[/tex] of the sphere is 24 centimeters, we substitute this value into the formula:
[tex]\[ V = \frac{4}{3} \pi (24)^3 \][/tex]
Carrying out the exponentiation:
[tex]\[ 24^3 = 24 \times 24 \times 24 = 13,824 \][/tex]
Next, we multiply this result by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ \frac{4}{3} \times 13,824 = 18,432.0 \][/tex]
Hence, the volume [tex]\( V \)[/tex] of the sphere is:
[tex]\[ V = 18,432.0 \pi \, \text{cm}^3 \][/tex]
So, the correct answer to fill in the blank is:
[tex]\[ 18,432.0 \, \text{cm}^3 \][/tex]
