To find the area of the pizza crust needed to fill the entire pan, we first need to calculate the area of the circular pizza pan. The area \( A \) of a circle can be calculated using the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.
Given that the diameter of the pizza pan is 15 inches, we can find the radius by dividing the diameter by 2:
\[ r = \frac{15 \text{ inches}}{2} = 7.5 \text{ inches} \]
Now we can substitute \( r \) into the area formula:
\[ A = \pi (7.5)^2 \]
Calculating \( (7.5)^2 \):
\[ (7.5)^2 = 56.25 \]
Now substitute this value back into the area formula:
\[ A = \pi \times 56.25 \]
To get a numerical approximation, we can use \( \pi \approx 3.14 \):
\[ A \approx 3.14 \times 56.25 \approx 176.625 \]
Thus, the area of the pizza crust needed to fill the entire pan is approximately:
\[ \boxed{176.63} \text{ square inches} \]
(Note: The exact area is \( 56.25\pi \) square inches, which is about 176.71 square inches if you use a more precise value of \( \pi \) such as 3.14159.)