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Advanced Math/Volume - Tank Follow-up


The tank is horizontal. Sorry for the omission.

My attempt:

3.1416 x 30 x 30 x 15 = 42411.6 cu. in.

42411.6 / 231 = 183.6 gal.

Where did I miscalculate?  Thanks again.

Since the tank is oriented horizontally, you can't use πrh to find the volume of gasoline.

Look at a vertical cross-section of the tank:

The surface of the gasoline is a chord of height h = 30 inches.
The chord subtends a central angle of θ = 2arccos((r-h)/r) ≅ 2.09 radians.
area of the segment (the portion with gasoline) = r(θ-sinθ)/2 ≅ 552.77 in

volume = 300 inches 552.77 in ≅ 165829.91 in

Convert volume from cubic inches to gallons:
165829.91 in (1 gallon)/(231 in) ≅ 717.88 gallons

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