Expert: Sherman D. - 5/30/2008

Question
A cylindrical tank is made of material 1.5 in. thick and has an outside circumference of 17 ft. 3.5 in.

Calculate capacity per ft. of height.

Not a homework question.

Thanks for your assistance.


Answer
since we only need the inside and not the outside to calculate volume.

C = 2pi * r

17ft 3.5in = 2pi * r

17ft 3.5in = (415/24)ft

r = (415/24)/(2pi)
r = 415/(48pi)

however we need to subtract from the thickness of the tank.

1.5in = (1/8)ft

r = (415/(48pi)) - (1/8)
r = (415/(48pi)) - (6pi/48)
r = (415 - 6pi)/(48pi)

V = Pi r^2h

V = pi * ((415 - 6pi)/(48pi))^2 * h
V = ((415 - 6pi)(415 - 6pi)/2304pi)h
V = ((172225 - 4980pi + 36pi^2)/2304pi)h

if you want to come close to the actual answer, then

V = about 21.6814h

More info found at http://mathforum.org/dr.math/faq/formulas/index.html