# How many cubic feet of water we need to fill a circular pool whose perimeter is 62.8 and the depth is 6 feet.

pohnpei397 | Certified Educator

We will need 1884 cubic feet of water to fill this pool.  Here is how to figure this out:

The volume of the pool is found by the area of the bottom multiplied by the depth of the pool.  First, we must find the area of the bottom.  The area of a circle is found by the formula A = pi*r^2.  So we must find the length of the radius.

We can find this because we know that the perimeter of a circle is equal to pi*diameter.  So

62.8 = pi*diameter or 62.8 = 3.14*diameter.  So now divide both sides by 3.14 and you get

diameter = 20

10^2 is 100.  So the area of the bottom of the pool is

A = 3.14*100 or A = 314.

So now we multiply the area by the depth of the pool.

314*6 = 1884

hala718 | Certified Educator

To find out how many cubic feet we need, we need to determine the volume of the pool.

The surface of the pool is a circle , then the pool has a cylinder shape

We know that the cylinder volume (v)= A * h

where A is the area of the circle and h is the height

We need to first to calculate the area (A)

A= Pi* r^2 where r is the radius

But we know that the Perimeter P= 62.8= 2*pi* r

==> r= 62.8 / 2*pi    (Pi=3.14)

==> r= 62.8/ 2(3.14)= 10

Then A = r^2 *pi = 100 (3.14) = 314

Then V = 314 * 6 = 1884 cubic feet

Then we need 1884 cubic feet of water to fill the pool.