Answer:
The 14-inch pizza cut into 8 slices.
Explanation:
The deep-dish pizza forms a cylindrical shape.
To make comparisons, we find the volume of each slice of pizza in each case.
[tex]\text{Volume of a cylinder=}\pi r^2h[/tex]Case 1
A 14-inch pizza that is 3 inches deep.
Radius = 14/2 = 7 inches
Height = 3 inches
[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times7^2\times3 \\ =147\pi\text{ cubic inches} \end{gathered}[/tex]Since it is cut into 8 slices:
[tex]\begin{gathered} \text{The volume of one slice=}\frac{147\pi}{8} \\ =18.375\pi\text{ cubic inches} \end{gathered}[/tex]Case 2
A 16-inch pizza that is 2 inches deep.
Radius = 16/2 = 8 inches
Height = 2 inches
[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times8^2\times2 \\ =128\pi\text{ cubic inches} \end{gathered}[/tex]Since it is cut into 7 slices:
[tex]\begin{gathered} \text{The volume of one slice=}\frac{128\pi}{7} \\ \approx18.285\pi\text{ cubic inches} \end{gathered}[/tex]Conclusion
The volume of a slice of pizza in the first case (the 14 -inch pizza cut into 8 slices) is larger, therefore it should be chosen to get the most food.
