The radius of the pool is 9.01 m.
Given,
In the question:
A circular pool is surrounded by a brick walkway 3 m wide.
The area of the walk- way is 198 m^2.
To find the Radius of the pool.
Now, According to the question:
"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".
Let R = Radius of the pool
Area of the circle bounded by the outside edge of the walkway is:
[tex]\pi[/tex](R +3)^2
Area of the pool is:
[tex]\pi R^2[/tex]
Now, Our equation is:;
[tex]\pi[/tex](R +3)^2 - [tex]\pi R^2[/tex] = 198
[tex]\pi[/tex]((R+3)^2 - [tex]R^2[/tex]) = 198
Open the inner bracket :
[tex]\pi[/tex]([tex]R^2+6R+9-R^2[/tex]) = 198
[tex]\pi[/tex](6R +9) = 198
6R+9 = 198/[tex]\pi[/tex]
6R = 198/[tex]\pi[/tex] - 9
R = (198/[tex]\pi[/tex] - 9)/6
R = (198/(3.14) - 9)/6
R = (63.057 - 9)/6
R = 54.057/6
R = 9.01 meters
Hence, The radius of the pool is 9.01 m.
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