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Depth of a Tank

Date: 09/04/97 at 13:08:29
From: Tyler Rossman
Subject: Finding the Depth of a Tank

Dear Dr. Math,

Hi. I am in the 5th grade. I have tried and tried for the right answer 
to this problem but I cannot find anything in my book to help me with 
it! Here is the problem:

You have a tank 100 feet long and 10 feet wide that holds a 
volume of 15,000 cubic feet of water. From this I have to find the 
depth of the tank. 

I would really appreciate your help with this.  

Thank you.

Tyler Rossman

Date: 09/10/97 at 12:23:38
From: Doctor Pipe
Subject: Re: Finding the Depth of a Tank


One way to solve this problem is to build the tank and fill it with 
15,000 cubic feet of water and then measure how deep the water is.  
But first, check with your parents about how much 15,000 cubic feet of 
water costs! 

Another way goes like this.

This problem is basically a volume problem. You know that the formula 
for calculating the volume of a rectangular tank is

          Volume = length x width x depth

only in this case, you have been given the volume, width, and length 
and have been asked to calculate the depth.

The tank has a length of 100 feet and a width of 10 feet - right? So 
if the tank is one foot deep, how many cubic feet of water does it 
hold? 100 x 10 x 1 = 1,000 cubic feet. Change the value for depth in 
the equation to a value that will result in the desired volume of 
15,000 cubic feet.

Another way would be to rewrite the Volume equation so that it is a 
depth equation:

          Depth = Volume / (length x width)

Do you understand how this is done? 

Now, if you substitute in the "givens", you get:

          Depth = 15,000 / (100 x 10)

You should get the same answer in both of the above cases ... and also 
if you actually build the tank ...

Hope this helps ... Good luck!

-Doctor Pipe,  The Math Forum
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Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
High School Practical Geometry
Middle School Geometry
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Middle School Word Problems

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