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# Advanced Math/Volume - Tank Follow-up

Question
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.

Randy
Since the tank is oriented horizontally, you can't use πr²h to find the volume of gasoline.

Look at a vertical cross-section of the tank: https://www.flickr.com/photos/dwread/22308321786/

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) = r²(θ-sinθ)/2 ≅ 552.77 in²

volume = 300 inches × 552.77 in² ≅ 165829.91 in³

Convert volume from cubic inches to gallons:
165829.91 in³ × (1 gallon)/(231 in³) ≅ 717.88 gallons

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