Question

A circular fountain has a circular walkway surrounding it with a width of 7 ft. The total area taken up by the walkway is 693π ft^2. Find the diameter of the pool.

Answer 1

check the picture below.

$\bf A=2\pi pw\quad \begin{cases} w=7\\ A=693\pi \end{cases}\implies 693\pi =2\pi p7\implies \cfrac{693\pi }{14\pi }=p \\\\\\ 49.5=p\\\\ -------------------------------\\\\ r=p-\cfrac{w}{2}\implies r=49.5-3.5\implies r=46$

now, that's just the radius of the pool, the diameter would be twice as much, or 2r.