What is the volume of an upright circular cylinder tank with a diameter of 12 feet when filled to a depth of 8 feet?

To find the volume of an upright circular cylinder tank, you use the formula for the volume of a cylinder, which is given by:

[ V = \pi r^2 h ]

In this formula, ( r ) is the radius of the cylinder, ( h ) is the height (or depth) of the cylinder, and ( \pi ) (approximately 3.14159) is a mathematical constant.

For the given tank:

• The diameter is 12 feet, which means the radius is half of that, so ( r = 12/2 = 6 ) feet.
• The depth (or height) to which the tank is filled is 8 feet.

Plugging these values into the formula:

1. Calculate the radius squared: [ r^2 = 6^2 = 36 ]

2. Now use the volume formula: [ V = \pi \times 36 \times 8 ]

3. Calculate the volume: [ V = \pi \times 288 ]

4. Using an approximation for ( \pi ): [ V \approx 3.14159 \times 288 \approx 904.32 \