Question

constructing a border around a pool a circular pool measures 10 feet across. one cubic yard of concrete is to be used to create a circular border of uniform with around the pool. if the border is to have a depth of 3 inches how wide will the border be

Answer 1

We get w = 1.508 feet.

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 =
`(3)/(12)=0.25 feet`

The circular area including pool and the border, radius =
`(w+5)`

Border area = Total area - pool area

=
`\pi (w+5)^(2) -\pi (5)^(2)`

Putting pi = 3.14 and solving the expression we get the following equation:

`3.14w^(2)+31.4w-53.5`

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.

`0.25(3.14w^(2)+31.4w-53.5) =27`

`=> 0.785w^(2)+7.85w-13.375-27= 0`

`=> 0.785w^(2)+ 7.85w-13.625= 0`

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.