Using similar triangles to solve a related rates problem

Question: If water is being pumped into the trough at 2 cubic feet per minute, how fast (in ft/min) is the water level rising when h is 1.4 feet deep?
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.A trough being filled with water. The trough is a triangular prism such that it is made of 2 triangles that are parallel to each other and 12 feet apart, and 2 sides that are rectangles that share an edge and also connect the two triangles. The mouth of the trough where the water is being poured is a rectangle was well. The height of the trough and triangles are 3 feet. The mouth of the trough and base of the triangle is 3 feet. The height of the water is labeled h feet. The water being poured in is labeled 2 cubic feet per minute.(a)If water is being pumped into the trough at 2 cubic feet per minute, how fast (in ft/min) is the water level rising when h is 1.4 feet deep?

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Answered By:

Richard C.
Confidence-building Geometry tutor with 18 years experience

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