A cyclinder cooling tank has an outside diameter of 6.00 ft. the wall on all sides are 5.00in thick and the tank is 10.0ft tall. how many gallons of water will this tank hold?

V=πr2h

V = 3.14 * 2.92^2 * 10

V = 3.14 * 8.52 * 10

V = 267.42 cubic feet
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1 cubic foot = 7.48052 gallons

7.48052 * 267.42 = _________ gallons

To calculate the capacity of a cylinder, we need to find the volume. The formula to calculate the volume of a cylinder is:

V = π × r^2 × h

Where:
V = Volume
π = Pi (approximately 3.14159)
r = Radius of the cylinder
h = Height of the cylinder

First, let's calculate the radius. The diameter is given as 6.00 ft, and since the wall thickness is included, we need to subtract twice the thickness from the diameter to get the inside diameter:

Inside Diameter = Outside Diameter - 2 × Wall Thickness
Inside Diameter = 6.00 ft - 2 × 5.00 in

Next, we need to convert the inside diameter to feet:

Inside Diameter = 6.00 ft - 2 × (5.00 in ÷ 12 in/ft)

Now we can calculate the radius by dividing the inside diameter by 2:

Radius = Inside Diameter ÷ 2

Next, we'll calculate the volume by substituting the values into the formula:

Volume = π × Radius^2 × Height

Finally, we need to convert the volume from cubic feet to gallons. There are 7.481 gallons in 1 cubic foot. Multiply the volume by this conversion factor to determine the total number of gallons the tank can hold.

Let's calculate the volume step by step:

1. Calculate the inside diameter:
Inside Diameter = 6.00 ft - 2 × (5.00 in ÷ 12 in/ft)

2. Calculate the radius:
Radius = Inside Diameter ÷ 2

3. Calculate the volume:
Volume = π × Radius^2 × Height

4. Convert the volume to gallons:
Total Gallons = Volume × 7.481

Plug in the numbers and follow these steps to find the answer.