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?
To find the volume of water that the tank can hold, we first need to calculate the internal dimensions of the tank. We can do this by subtracting the thickness of the tank walls from the external dimensions.
Given:
- Outside diameter of the tank = 6.00 ft
- Wall thickness = 5.00 in
- Tank height = 10.0 ft
Converting the wall thickness to feet:
1 inch = 1/12 ft
Wall thickness = 5.00 in × (1 ft/12 in) = 0.4167 ft
Calculating the inner diameter of the tank:
Inner diameter = Outside diameter - 2 × Wall thickness
Inner diameter = 6.00 ft - (2 × 0.4167 ft) = 5.1666 ft
Now, we can calculate the volume of the tank using the formula for the volume of a cylinder:
Volume = π × (radius^2) × height
Calculating the radius:
Radius = Inner diameter/2 = 5.1666 ft/2 = 2.5833 ft
Substituting the values into the volume formula:
Volume = π × (2.5833 ft)^2 × 10.0 ft
Volume ≈ 210.158 ft^3
Finally, to convert the volume to gallons, we need to multiply by the conversion factor:
1 cubic foot = 7.48052 gallons
Gallons = Volume × 7.48052
Gallons ≈ 210.158 ft^3 × 7.48052 gallons/ft^3
Therefore, the tank will hold approximately 1,570.1 gallons of water.