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
