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

[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?

 

[Teacherman657]

Nevermind! Got it!

 

[Mark44]

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.