Posted by Kristen on Tuesday, April 21, 2009 at 3:28pm.
Think of the grain storage tank as two independent, but related, geometric figures for solving this problem. You have a cylinder with only a bottom (no top because it's covered by the half sphere) and a sphere that's cut across the middle (i.e., half sphere).
The surface area formula for a cylinder with no top is pi*r^2 + 2*pi*r*h.
The surface area formula for half a sphere is (1/2)*4*pi*r^2 = 2*pi*r^2.
The volume area formula for a cylinder is pi*r^2*h.
The volume area formula for half a sphere is (1/2)*4/3*pi*r^3 = 3/2*pi*r^3.
Since the diameter is 80 feet, the radius is 1/2 the diameter or 40 feet.
Therefore, the surface area of the grain storage tank is pi*r^2 + 2*pi*r*h + 2*pi*r^2 = 27,632 sq/ft.
The volume of the grain storage tank is pi*r^2*h + 3/2*pi*r^3 = 552,640 cu/ft.
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