A trough has vertical ends that are equilateral triangles with sides of length 2 ft. If the trough is filled with water to a depth of 1 ft, find the force exerted by the water on one end of the trough. Round to one decimal place. (The weight density of water is 62.4 lb/ft³.) A)12.0 lb B)62.4 lb C)6.0 lb D)31.2 lb

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Quizplus · Accepted Answer

The force exerted by the water on one end of the trough is equal to the weight of the water in the trough. The volume of the water in the trough is equal to the area of the end of the trough times the depth of the water. The area of the end of the trough is equal to the area of an equilateral triangle with sides of length 2 ft. The area of an equilateral triangle is equal to (sqrt(3)/4)s^2, where s is the length of a side. Therefore, the area of the end of the trough is (sqrt(3)/4)(2 ft)^2 = 2 sqrt(3) ft^2. The depth of the water is 1 ft. Therefore, the volume of the water in the trough is 2 sqrt(3) ft^2 * 1 ft = 2 sqrt(3) ft^3. The weight density of water is 62.4 lb/ft^3. Therefore, the weight of the water in the trough is 62.4 lb/ft^3 * 2 sqrt(3) ft^3 = 12.0 lb.

A Trough Has Vertical Ends That Are Equilateral Triangles with Sides