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

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 = $\frac{3}{12}=0.25 feet$

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.