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A storage tank for propane gas is to be constructed in the shape of a right circular cylinder of altitude 20 feet with a hemisphere attached to each end. determine the radius x so that the resulting volume is 216Ï€ ft3.

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gvcci
Volume for a right circular cylinder = 
V = (π)(r^2)(h) where 
V = right circular cylinder volume 
π = the constant pi 
r = radius 
h = height or altitude 

With a hemisphere on each end, if I calculate the volume of a sphere, that will include both hemispheres. So the volume of a sphere = 
V = (4/3)(π)(r^3) where 
V = sphere volume 
π = the constant pi 
r = radius 

So the total volume of the entire propane gas storage tank = 
Vt = volume of cylinder + 2(volume of hemishere) 
Vt = volume of cylinder + volume of sphere 
Vt = (π)(r^2)(h) + (4/3)(π)(r^3) 
216π = (π)(r^2)(20) + (4/3)(π)(r^3) 
Divide both sides by π to eliminate it. 
216 = 20r^2 + (4r^3)/3 
Multiply both sides of the equal sign by 3 to eliminate the denominator. 
648 = 60r^2 + 4r^3 
Factor a common 4 from the right side of the equal sign. 
648 = 4(15r^2 + r^3) 
162 = (15r^2 + r^3) 
r = 3