Problem:
A cylindrical tank with radius feet and height feet is lying on its side. The tank is filled with water to a depth of feet. What is the volume of the water, in cubic feet?
Answer Choices:
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Solution:
The portion of each end of the tank that is under water is a circular sector with two right triangles removed as shown. The hypotenuse of each triangle is , and the vertical leg is , so each is a triangle. Therefore the sector has a central angle of , and the area of the sector is
The area of each triangle is , so the portion of each end that is underwater has area . The length of the cylinder is , so the volume of the water is
The problems on this page are the property of the MAA's American Mathematics Competitions