[tex]16\text{ }\pi\text{ y}[/tex]
Explanation
Step 1
the area of a circle is given by:
[tex]\begin{gathered} \text{Area}_c=\pi r^2 \\ \text{where r is the radius} \end{gathered}[/tex]
so, the area of teh walkway will be the difference of areas
[tex]\begin{gathered} A_{walkway}=A_{entire\text{ circle}}-Area_{pool} \\ \text{replace} \\ A_{walkway}=\pi(y+4)^2-\pi(y-4)^2 \end{gathered}[/tex]
Step 2
expand the polynomius:
[tex]\begin{gathered} A_{walkway}=\pi(y+4)^2-\pi(y-4)^2 \\ A_{walkway}=\pi(y^2+8y+16)^{}-\pi(y^2-8y+16) \\ A_{walkway}=\pi(y^2+8y+16)^{}-\pi(y^2-8y+16) \\ A_{walkway}=\pi(y^2+8y+16-(y^2-8y+16)) \\ A_{walkway}=\pi(y^2+8y+16-y^2+8y-16)) \\ A_{walkway}=\pi(16y) \\ \end{gathered}[/tex]
therefore, the answer is
[tex]16\text{ }\pi\text{ y}[/tex]
I hope this helps you
