Answer :
Answer:
Step-by-step explanation:
To find the volume \( V \) of a sphere when given the diameter \( d \), we use the formula:
\[ V = \frac{4}{3} \pi \left(\frac{d}{2}\right)^3 \]
Given that the diameter \( d \) of the sphere is 16 inches, we first calculate the radius \( r \):
\[ r = \frac{d}{2} = \frac{16}{2} = 8 \text{ inches} \]
Now substitute \( r = 8 \) inches and \( \pi = 3.14 \) into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (8)^3 \]
Calculate \( (8)^3 \):
\[ (8)^3 = 8 \times 8 \times 8 = 512 \]
Now substitute \( 512 \) into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 512 \]
Calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 = 4.1867 \]
Now multiply by \( 512 \):
\[ V = 4.1867 \times 512 \]
\[ V = 2144.7424 \]
Round the volume to the nearest hundredth:
\[ V \approx \boxed{2144.74} \text{ cubic inches} \]
Therefore, the volume of the sphere, rounded to the nearest hundredth, is \( \boxed{2144.74} \) cubic inches.
