Question

A circular pool is surrounded by a circular walkway. The radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4. Write a polynomial that represents the area of just the walkway itself, not including the space covered by the pool.
1. 16πy
2. 32
3. −16πy
4. 16πy + 32

Answer 1

A=πr²

pool=π(y-4)²=π(y²-8y+16)
total=π(y+4)²=π(y²+8y+16)

walkway=total-pool
walkway=π(y²+8y+16)-π(y²-8y+16)=
π(y²+8y+16-y²+8y-16)=
π(16y)=
16πy
first option is answer