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

So the volume of water in the trough is V=A*h where A is the area of the water and h is the height of the water. So the formula for the area of a triangle is A=(1/2)bh where b is the base of the triangle and h is the height. In this case, the base is the length of the trough (15ft) and the height is the depth of the water (2ft). In summary, the water level is rising at a rate of 2.5 ft3/min when the depth of the water is 2 ft.
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iRaid
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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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Edit: Attached picture
 
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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.
 

1. What is the concept of related rates in terms of water level?

Related rates is a concept in calculus that involves finding the rate of change of one quantity with respect to another when the two quantities are related. In the context of water level, this means finding the rate at which the water level is changing at a specific point in time.

2. How is the rate of change of water level calculated?

The rate of change of water level is calculated using the chain rule from calculus. This involves taking the derivative of the water level function with respect to time and multiplying it by the rate of change of time. In simpler terms, it is the product of the change in the water level and the change in time.

3. What are some real-life applications of related rates in water level?

Related rates in water level can be applied in various real-life situations, such as determining the rate of filling or draining of a tank, measuring the flow rate of a river or stream, and calculating the rate of evaporation from a swimming pool or lake.

4. How can related rates of water level be used to solve problems?

In order to solve problems involving related rates of water level, it is important to first identify the quantities that are changing and how they are related. Then, using the chain rule and other calculus techniques, the rate of change of the water level can be calculated and used to solve the problem at hand.

5. What are some common mistakes to avoid when solving related rates problems involving water level?

When solving related rates problems involving water level, it is important to pay attention to the units of measurement and make sure they are consistent. It is also important to properly set up the equations and identify the variables that represent the changing quantities. Additionally, it is important to carefully differentiate the equations using the chain rule and avoid common errors such as taking the derivative of a constant.

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