To determine the volume of a sphere with a radius of 24 centimeters, we use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Here, \( r \) represents the radius of the sphere. Given that \( r = 24 \) cm, we substitute this value into the formula:
[tex]\[ V = \frac{4}{3} \pi (24)^3 \][/tex]
First, we calculate \( 24^3 \):
[tex]\[ 24^3 = 24 \times 24 \times 24 = 13824 \][/tex]
Next, we multiply 13824 by \( \frac{4}{3} \):
[tex]\[ \frac{4}{3} \times 13824 = 18432 \][/tex]
Thus, the volume of the sphere is:
[tex]\[ V = 18432 \pi \][/tex]
So, the volume of the sphere is \( 18432\pi \) cubic centimeters.
To fill in the blank in the given equation, the correct answer is:
A sphere has a radius of 24 centimeters. What is its volume?
[tex]\[ V = \boxed{18432 \pi} \ \text{cm}^3 \][/tex]
