To calculate the volume of a sphere, we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere. First, we need to find the radius from the diameter.
Given that the diameter is 7 inches, the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{7}{2} = 3.5 \text{ inches} \]
Now we can substitute \( r \) and \( \pi \) (approximated as 3.14) into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (3.5)^3 \]
First, calculate \( (3.5)^3 \):
\[ (3.5)^3 = 3.5 \times 3.5 \times 3.5 = 12.25 \times 3.5 = 42.875 \]
Now substitute this value into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 42.875 \]
Calculate \( 3.14 \times 42.875 \):
\[ 3.14 \times 42.875 \approx 134.2855 \]
Now multiply by \( \frac{4}{3} \):
\[ V \approx \frac{4}{3} \times 134.2855 \approx 178.714 \]
Finally, rounding to the nearest tenth:
\[ V \approx 178.7 \text{ inches}^3 \]
Thus, the volume of the sphere is approximately \( \boxed{178.7} \) inches³.