The volume of the cylindrical tank can be calculated using the formula V = πr^2h, where r is the radius (half the diameter) and h is the height (length of the tank).
A) First, we need to convert the dimensions to feet:
- Diameter = 20ft
- Radius = 10ft
- Length = 22ft
- Depth of water = 6ft
Using the formula for the volume of a cylinder, we get:
V = πr^2h
V = π(10ft)^2(22ft)
V = 6,853.98 cubic feet
To convert cubic feet to gallons, we need to multiply by 7.48 (since 1 gallon = 7.48 cubic feet). So:
6,853.98 cubic feet x 7.48 gallons/cubic foot = 51,291.79 gallons
Therefore, there are approximately 51,292 gallons of water in the tank.
B) The total volume of the tank is:
V = πr^2h
V = π(10ft)^2(22ft)
V = 6,853.98 cubic feet
To find how much more water is needed to fill the tank to capacity, we need to subtract the volume of water already in the tank (which we calculated in part A) from the total volume of the tank. So:
6,853.98 cubic feet x 7.48 gallons/cubic foot - 51,291.79 gallons = 22,048.21 gallons
Therefore, it will take approximately 22,048 gallons of water to fill the tank to capacity.