Find the volume of water required to fill a pool with a diameter of 6m and a height of 2m. Keep in mind that the water must travel through a hose before it goes into the pool. Assume the hose is a perfect cylinder. The length of the hose is 8m and the diameter of the inner tubing of the hose is 2cm. Round to the nearest hundredth.

I will assume that the pool is a cylinder.

volume = π r^2 h
= π(9)(2) = 18π

What does the hose have to do with it?
Was there supposed to be some rate of flow ?

To find the volume of water required to fill the pool, we need to calculate the volume of both the pool and the hose.

First, let's calculate the volume of the pool. The pool is shaped like a cylinder, so we can use the formula for the volume of a cylinder:

Volume of a cylinder = π * radius^2 * height

The diameter of the pool is given as 6m, so the radius is half of that, which is 3m. The height of the pool is given as 2m. Plugging these values into the formula, we get:

Volume of the pool = π * (3m)^2 * 2m
= π * 9m^2 * 2m
= 18π m^3

Next, let's calculate the volume of the hose. The hose is also shaped like a cylinder, so we can use the same formula:

Volume of a cylinder = π * radius^2 * height

We are given the diameter of the inner tubing of the hose as 2cm, so the radius is half of that, which is 1cm. However, we need to convert this to meters since the measurements of the pool are in meters. There are 100 centimeters in a meter, so the radius of the hose is 1cm / 100 = 0.01m. The length of the hose is given as 8m. Plugging these values into the formula, we get:

Volume of the hose = π * (0.01m)^2 * 8m
= π * (0.0001m^2) * 8m
≈ 0.00251π m^3

Now, to find the total volume of water required, we add the volume of the pool and the volume of the hose:

Total volume = Volume of the pool + Volume of the hose
= 18π m^3 + 0.00251π m^3
≈ 18.00251π m^3

Finally, to round to the nearest hundredth, we can approximate π to 3.14 and calculate the answer:

Total volume ≈ 18.00251 * 3.14 m^3
≈ 56.5702874 m^3

Rounded to the nearest hundredth, the volume of water required to fill the pool is approximately 56.57 m^3.