The hopper bin in the picture below is modeled by the two-dimensional figure beside it. The hopper bin is composed of a cylinder, and 2 EQUAL cones. Let d be the center of the base of the cone.
52° cylinder cones
The diameter of the hopper is 36 ft and the height of the cylindrical portion is 20 ft. The measure of the acute
angle formed by the slant height of the cone and its base is 52°, determine and state, to the nearest cubic foot,
the volume of the hopper bin.
The hopper bin was constructed to hold a maximum of 500,000 pounds of feed. If feed weighs 22 pounds per cubic foot, can the carnival tent be filled to 85% of its volume and not exceed the weight limit? Justify your
answer.