How can the water level in a trough be calculated using related rates?

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SUMMARY

The discussion focuses on calculating the water level in a trough using related rates, specifically for a trough that is 15 feet long and has an isosceles triangular cross-section with a height of 3 feet. The water enters the trough at a rate of 2.5 cubic feet per minute. To determine how fast the water level rises when it is 2 feet deep, participants emphasize the need to calculate the area of the water's surface rather than the volume of the entire triangular prism. The correct approach involves using the formula for the volume of a triangular prism and the relationship between volume and height.

PREREQUISITES
  • Understanding of related rates in calculus
  • Familiarity with the volume formula for triangular prisms
  • Knowledge of how to derive relationships between different geometric dimensions
  • Basic skills in solving differential equations
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  • Study the concept of related rates in calculus
  • Learn how to derive the volume of a triangular prism based on varying dimensions
  • Explore examples of similar problems involving water flow and geometric shapes
  • Practice solving differential equations related to volume and height changes
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Students studying calculus, particularly those focusing on related rates, as well as educators seeking to explain geometric applications in real-world scenarios.

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Homework Statement


12.) A trough is 15ft long and 4ft across the top as shown in the figure. Its ends are isosceles triangles with height 3ft. Water runs into the trough at the rate of 2.5 ft3/min. How fast is the water level rising when it is 2 ft deep?

Homework Equations


The Attempt at a Solution



Not sure how to do this..
dv/dt = 2.5

I tried using the volume of a triangular prism: V=(1/2)bhl but no success.. I think the problem is IDK which numbers to use for the volume equation?
Can someone point me in the correct direction?
 

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If anyone is looking at this, what you have to do is find the area of the water, not the actual triangular prism.
 

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