# Related Rates: Finding the Rate of Change of Water Depth in a Pyramid Tank

• Teacherman657
In summary, the problem involves a pyramid-shaped tank with a square base of 12 feet and a vertex 10 feet above the base. The tank is filled to a depth of 4 feet and water is flowing into it at a rate of 2 cubic feet per minute. Using the formula for the volume of a pyramid, V=(1/3)Bh, we can find the rate of change of the depth of water in the tank to be 25/648. However, the person asking the question got a different answer of 25/162 and is unsure if the book made a mistake. They later confirmed that they had made a mistake in their calculations.
Teacherman657
The base of a pyramid-shaped tank is a square with sides of length 12 feet, and the vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at the rate of 2 cubic feet per minute. Find the rate of change of the depth of water in the tank. (Hint: The volume of a pyramid is given by V=(1/3)Bh where B is the area of the base and h is the height of the pyramid.)

The answer in the back of the book is 25/648.

I got 25/162.

I think the book made a mistake, but I'm not sure. Can I get any confirmation?

Nevermind! Got it!

Teacherman657 said:
The base of a pyramid-shaped tank is a square with sides of length 12 feet, and the vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at the rate of 2 cubic feet per minute. Find the rate of change of the depth of water in the tank. (Hint: The volume of a pyramid is given by V=(1/3)Bh where B is the area of the base and h is the height of the pyramid.)

The answer in the back of the book is 25/648.

I got 25/162.

I think the book made a mistake, but I'm not sure. Can I get any confirmation?

In the future, if you work a problem and get a different answer than the book's answer, please show the work you did to get your answer. Telling us that you got one answer and the book got another answer forces us to work the problem, which could be more usefully spent helping someone else who has shown his or her work.

## 1. What are related rates?

Related rates refer to the change in one variable with respect to another variable. In other words, it is the rate at which one quantity changes in relation to the change in another quantity.

## 2. How do you solve related rates problems?

The key to solving related rates problems is to first identify the variables and how they are related to each other. Then, use the given information and the chain rule to set up an equation and solve for the desired rate.

## 3. What is the chain rule?

The chain rule is a calculus rule that allows us to find the derivative of a composite function. In related rates problems, it is used to find the rate of change of one variable with respect to another variable.

## 4. What are some common applications of related rates?

Related rates have many real-world applications, such as in physics, engineering, and economics. Some common examples include rates of change in distance, volume, and temperature.

## 5. What are some tips for solving related rates problems?

One helpful tip is to draw a diagram to visualize the problem and the relationship between the variables. It is also important to clearly label the variables and their rates. Additionally, breaking down the problem into smaller, simpler steps can make it easier to solve.

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