Question 169634
<font color = "red" size = 7><b>Edwin's solution with drawings:
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A circular pool is 46 feet in diameter and has a flag stone walk around it that is 4 feet wide. Find the area of the walk. Express the answer in terms of {{{pi}}}.
<pre><font size = 4 color = "indigo"><b>
Here is the pool only, which is 46 feet across.

{{{drawing(400,400,-3,3,-3,3, circle(0,0,2.3),
line(-2.3,0,2.3,0), locate(0,0,"d=46"))}}}

So it has a radius of half that, or 23 feet:

{{{drawing(400,400,-3,3,-3,3, circle(0,0,2.3),
line(0,0,2.3,0), locate(1,0,"r=23"))}}}

The area of the pool is given by the formula

{{{A = pi*r^2=pi*23^2=529pi}}}

It has a walk around it which is 4 feet wide.

{{{drawing(400,400,-3,3,-3,3, circle(0,0,2.3), circle(0,0,2.7),
line(0,0,2.7,0), locate(1,0,"r=23"),locate(2.4,0,4))}}}

If we take out the inner circle, like this:

{{{drawing(400,400,-3,3,-3,3, circle(0,0,2.7),
line(0,0,2.7,0), locate(1,0,"r=23"),locate(2.4,0,4),
line(2.3,-.1,2.3,.1)

)}}}

we see that the outer circle, which includes both the
pool and the walk, has a radius of 
{{{23+4}}} or {{{27}}} feet.

{{{drawing(400,400,-3,3,-3,3, circle(0,0,2.7),
line(0,0,2.7,0), locate(1.15,0,"r=27"))}}}

The area of the outer circle which includes
the pool and the walk is given by the formula:

{{{A = pi*r^2=pi*27^2=729pi}}}

Going back to the original picture:

{{{drawing(400,400,-3,3,-3,3, circle(0,0,2.3), circle(0,0,2.7),
line(0,0,2.7,0), locate(1.15,0,23),locate(2.4,0,4))}}}

AREA OF WALK = AREA OF OUTER CIRCLE - AREA OF INNER CIRCLE =

{{{729pi-529pi}}}

{{{200pi}}} square feet.

Edwin</pre>