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geometry

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A grain storage tank is in the shape of a cylinder covered by half a sphere. The height of the cylinder is 50 feet and its diameter is 80 feet. find the total surface area (including the base) and volume of the tank.

  • geometry - ,

    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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