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 216π ft3.
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
