How many gallons of Oil would be in a cylindrical tank that was 24 feet long and had a diameter of 6 feet if the oil was 6 inches deep at the bottom of the tank?
I am wondering if the tank axis is horizontal, or vertical?
To calculate the number of gallons of oil in a cylindrical tank, we need to follow a few steps:
Step 1: Calculate the volume of the cylindrical tank.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. Since the diameter of the tank is given, we need to convert it to the radius by dividing it by 2. Thus, the radius (r) = 6 ft / 2 = 3 ft, and the height (h) = 24 ft.
Step 2: Convert the volume to cubic inches.
Since the depth of the oil is given in inches, we need to convert the volume to cubic inches for consistency. Since 1 ft = 12 inches, the new volume (V) would be V = π(3 ft)²(24 ft) × 12 inches/ft × 12 inches/ft × 12 inches/ft.
Step 3: Convert the volume to gallons.
To convert the volume from cubic inches to gallons, divide the volume by the conversion factor. There are 231 cubic inches in 1 gallon. So, the number of gallons (G) would be G = V / 231.
Let's calculate it:
Step 1: V = π(3 ft)²(24 ft) = 216π cubic feet.
Step 2: V = 216π × 12 inches/ft × 12 inches/ft × 12 inches/ft = 216π × 1728 cubic inches.
Step 3: G = (216π × 1728) / 231 = 12288π / 231.
To get the actual value, we can calculate the approximate value by evaluating the expression:
G ≈ 53.27 gallons.
Therefore, there would be approximately 53.27 gallons of oil in the cylindrical tank.