Given the information, we have the following circle shaped pizza:
we can use the following equation for the area of a circle:
![A=\pi\cdot r^2](https://img.qammunity.org/2023/formulas/mathematics/college/c3j55td07q4b6rf8hxaebd9fh4afvxzn0d.png)
in this case, since the diameter is d = 8in, the radius is:
![\begin{gathered} r=(d)/(2)=(8)/(2)=4 \\ \Rightarrow r=4 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/jmeqhxz39lo9waqf4yd1cih6vyobfza54n.png)
then, using the formula, we get:
![\begin{gathered} A=\pi\cdot(4)^2=(3.1416)(16)=50.2656 \\ \Rightarrow A=50.3in^2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/pmmuyb4cjmqi75gfsgxsny5lr6dy86249k.png)
therefore, the area of the small pizza is 50.3 square inches