Question

find the volume of the solid to the nearest cubic centimeter. (assume ( r = 24 ).)

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume \( V \) of a sphere is \( V=\frac{4}{3}\pi r^{3} \).

Step2: Substitute \( r = 24 \) into the formula

Substitute \( r = 24 \) into \( V=\frac{4}{3}\pi r^{3} \), we get \( V=\frac{4}{3}\pi(24)^{3} \).
First, calculate \( (24)^{3}=24\times24\times24 = 13824 \).
Then, \( V=\frac{4}{3}\pi\times13824 \).
\(\frac{4}{3}\times13824 = 4\times4608=18432\).
So \( V = 18432\pi \).

Step3: Calculate the numerical value

Take \( \pi\approx3.14159 \).
\( V\approx18432\times3.14159\).
\(18432\times3.14159 = 18432\times(3 + 0.14159)=18432\times3+18432\times0.14159\).
\(18432\times3 = 55296\), \(18432\times0.14159\approx18432\times0.14 = 2580.48\) (a rough estimate for calculation, more accurately \(18432\times0.14159 = 2609.7\)).
\(V\approx55296+2609.7=57905.7\approx57906\).

Answer:

\(57906\)