Question

Question 3: 12 ptsA circular pool is surrounded by a circular walkway. The radius of the pool is y - 4 and the radius of the full circleformed by the walkway is y + 4. Write a polynomial that represents the area of just the walkway itself, notincluding the space covered by the pool.The area of a circle is given by A = r7?, where r represents the radius of the circle.)O 16ny + 32O 16TyO-16nyO 32

Answer 1

`16\text{ }\pi\text{ y}`

Step-by-step explanation

Step 1

the area of a circle is given by:

`\begin{gathered} \text{Area}_c=\pi r^2 \\ \text{where r is the radius} \end{gathered}`

so, the area of teh walkway will be the difference of areas

`\begin{gathered} A_(walkway)=A_{entire\text{ circle}}-Area_(pool) \\ \text{replace} \\ A_(walkway)=\pi(y+4)^2-\pi(y-4)^2 \end{gathered}`

Step 2

expand the polynomius:

`\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}`

therefore, the answer is

`16\text{ }\pi\text{ y}`

I hope this helps you