The problem asks us to find the number of gallons needed to fill a cylindrical pool given its diameter, height, and the conversion factor between cubic feet and gallons. The pool has a diameter of 22 feet, a height of 4.2 feet, and 1 cubic foot holds 7.48 gallons. We are asked to round the answer to the nearest tenth.

1. Problem Description

The problem asks us to find the number of gallons needed to fill a cylindrical pool given its diameter, height, and the conversion factor between cubic feet and gallons. The pool has a diameter of 22 feet, a height of 4.2 feet, and 1 cubic foot holds 7.48 gallons. We are asked to round the answer to the nearest tenth.

2. Solution Steps

The volume $V$ of a cylinder is given by the formula:

$V = \pi r^2 h$

where $r$ is the radius and $h$ is the height.

The diameter is given as 22 feet, so the radius is $r = \frac{22}{2} = 11$ feet.

The height is given as $h = 4.2$ feet.

Plugging these values into the formula, we get:

$V = \pi (11^2)(4.2) = \pi (121)(4.2) = 508.2\pi \approx 1596.150657$ cubic feet.

We are given that 1 cubic foot holds 7.48 gallons, so we multiply the volume in cubic feet by 7.48 to find the volume in gallons:

$1596.150657 \times 7.48 \approx 11940.20191$ gallons.

Rounding the result to the nearest tenth gives 11940.2 gallons.

3. Final Answer

11940.2 gallons