To find the area of the base (B) of a cylinder, we use the formula for the area of a circle, which is:
\[ B = \pi r^2 \]
Where \( r \) is the radius of the base.
If the diameter of the cylinder is given as 14 inches, then the radius \( r \) is half of that:
\[ r = \frac{14}{2} = 7 \text{ inches} \]
Now, substituting this radius into the formula for the area of a circle:
\[ B = \pi (7)^2 \]
Therefore, the correct expression for finding the value of B, in square inches, for this cylinder is:
π(7)² (which corresponds to the first response option: pi times 7 squared)