Answer:
We get w = 1.508 feet.
Step-by-step explanation:
Let w be the width of the border.
The diameter of the pool will be 10 feet.
The depth will be 3 inches. So, we will convert it to feet.
3 inches = [tex]\frac{3}{12}=0.25 feet[/tex]
The circular area including pool and the border, radius =[tex](w+5)[/tex]
Border area = Total area - pool area
= [tex]\pi (w+5)^{2} -\pi (5)^{2}[/tex]
Putting pi = 3.14 and solving the expression we get the following equation:
[tex]3.14w^{2}+31.4w-53.5[/tex]
As given one cubic yard of concrete is to be used, this is the volume to be used.
1 cubic yard = 27 cubic feet
Now using the volume given and thickness of this area that is 0.25 feet.
[tex]0.25(3.14w^{2}+31.4w-53.5) =27[/tex]
[tex]=> 0.785w^{2}+7.85w-13.375-27= 0[/tex]
[tex]=> 0.785w^{2}+ 7.85w-13.625= 0[/tex]
Solving this quadratic equation, we get w = 1.508 feet and w = -11.508 feet.
Neglecting the negative value, we get w = 1.508 feet.
