SOLUTION: A circular pool is surrounded by a brick walkway 3m wide. Find the radius of the pool if the area of the walkway is 198 m^2.
The walkway is 3 m wide, and A of walkway = 193 m
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Question 509424: A circular pool is surrounded by a brick walkway 3m wide. Find the radius of the pool if the area of the walkway is 198 m^2.
The walkway is 3 m wide, and A of walkway = 193 m^2....
I think I need to find the area of the entire circle and subtract the area of the walkway from it, and figure out the radius from there, but I have no idea how to do so.
I'D LOVE any additional advice on polynomial word problems - rate-time-distance problems, problems involving area...
Any tips, please??
Much appreciated! Thank you !!
Found 2 solutions by solver91311, oberobic:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the radius of the pool. Then the radius of the entire circle including the walkway is 
. Then the area of the entire circle, including both the pool and the walkway is ^2)
, whereas the area of just the pool is 
. Subtract the area of the pool from the area of the entire circle to get the area of the walkway:
^2\ -\ \pi{r^2}\ =\ 198)
You can take it from here. Leave your answer in terms of 
for an exact answer or round your numeric approximation to the nearest whole meter since the precision of your given measurement was to the nearest square meter. Or, if you use the old standby 
as an approximation of then your answer comes out to be a whole number anyway.
John
My calculator said it, I believe it, that settles it
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The walkway and pool are circular, so the inside circumference of the walkway is less than the outside circumference. So, you can take the area of the inner circle (which is the pool, actually) and subtract it from the area of the outer circle.
.
pi*r^2 = area of the pool
.
pi*(r+3)^2 = area of the pool + walkway
.
pi*r^2 = pi*(r+3)^2 - 198
.
pi*r^2 = pi*(r^2 +6r +9) - 198
.
pi*r^2 = pi*r^2 + pi*6r + pi*9 -198
.
0 = pi*6r + pi*9 -198
.
pi*6r + pi*9 = 198
.
pi*(6r + 9) = 198
.
6r + 9 = 198/pi = 63.0253575
.
6r = 63.0253575 -9 = 54.0253575
.
r = 54.0253575/6
.
r = 9.00422624
.
r+3 = radius to outer edge of walkway
.
r+3 = 12.00422624
.
inner area = pi*(9.00422624^2)
inner area = 254.708049
.
outer area = pi*(12.00422624^2)
outer area = 452.708049
.
walkway area = 452.708049 - 254.708049 = 198
.
Correct.
.
Answer: The radius of the pool is 9.00422624 or about 9 meters.
.
Done.
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