SOLUTION: please help me with the following problem =http://postimage.org/image/y8wymavmx/

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Question 651053: please help me with the following problem =http://postimage.org/image/y8wymavmx/
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
The overall radius of the tank = (r+1)
:
Find the volume of the base
Vb = pi%2A%28r%2B1%29%5E2%2A1
The volume of the outer part is overall vol - inner volume
Vo = pi%2A%28r%2B1%29%5E2%2Ah - (pi%2Ar%5E2%2Ah)
Factor out pi*h
Vo = pi%2Ah%28%28r%2B1%29%5E2+-+r%5E2%29
FOIL (r+1)(r+1)
Vo = pi%2Ah%28r%5E2+%2B+2r+%2B+1+-+r%5E2%29
:
Vo = pi%2Ah%282r+%2B+1%29
:
Volume of outer plus base = 100 cu/ft
pi%2Ah%282r%2B1%29 + pi%2A%28r%2B1%29%5E2%2A1 = 100
Divide by pi
h%282r%2B1%29 + %28r%2B1%29%5E2%2A1 = 31.831
h%282r%2B1%29 + r%5E2%2B2r%2B1 = 31.831
h(2r+1) = 31.831 - r^2 - 2r - 1
h = %28-r%5E2+-+2r+%2B+30.831%29%2F%282r%2B1%29
:
(b)
V = pi%2Ar%5E2%2A%28%28-r%5E2+-+2r+%2B+30.831%29%2F%282r%2B1%29%29
:
(c)

Max vol = 65 cu/ft; r = 2.75; h = 2.73