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Asked by maham237 @ 12/01/2021 in Mathematics viewed by 297 People

Please Help!! A septic tank has the shape shown in the figure. How many gallons does it hold? (1 cu ft = 7.48 gallons.) (Round to the nearest gallon)

Answered by maham237 @ 12/01/2021

The overall volume is the sum of the volume of a cylinder of height 5'9" and diameter 3'6", and a sphere of diameter 3'6" (two hemispheres = full sphere).

Volume of the cylinder = (area of the base) x (height) = pi * (diameter/2)^2 * 5.75ft = 3.1415 * (3.5ft/2)^2 * 5.75 ft = 55.32 ft^3

Volume of the sphere = 4/3 * pi * (3.5ft)^3 / 8 = 22.45 ft^3

Total volume = (Volume of cylinder) + (Volume of sphere) = (55.32 + 22.45) ft^3 = 77.77 ft^3

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