A manufacturer of large enclosed cylindrical water tanks wants to know what dimensions the tanks should be in order to minimize the amount of material used. In order to find the dimensions, first consider a 10,000 litre tank (10 cubic metres). Using the formula for the volume of a cylinder, express the height of the tank (h metres) in terms of the radius (r metres).

Question

e.mccormick · Answer

Do you know the formula for the volume of a cylinder?

anonymous · Answer

pi*h*r^2

e.mccormick · Answer

So, you have $10=\pi hr^2$ with the given information.  Right?  So how would you "xpress the height of the tank (h metres) in terms of the radius (r metres)" at that point?  You solve for what?

anonymous · Answer

Solve for radius? I was unsure of what is meant by "express in terms of" when related to formulas.

e.mccormick · Answer

No, solve for Height.  You want a function of height that uses the radius.

e.mccormick · Answer

So with this one, it is not too hard.  Since everything on the right hand side is multiplied, just divide through by everything other than height.

anonymous · Answer

Ok makes sense, cheers for that @e.mccormick

e.mccormick · Answer

The typical formula is y in terms of x, so y=x+2 or whatever.  Whenever it is a in terms of b, the a part is alone and the b gets mixed with everything else.  If you remember that much, that part won't be too hard.  In fact, it follows the order we typically put the = sign.  f(x)=x+2, where f(x) means y is... so the y side in terms of the right hand side.

anonymous · Answer

So h = 10/(pi)r^2

e.mccormick · Answer

Yah.  That is how it would typically be written.

anonymous · Answer

Awesome dude, question well and truly answered.

e.mccormick · Answer

Good!  Have fun!

e.mccormick · Answer

Now that I have my $\LaTeX$ working properly again...

$$\large h = \frac{10}{\pi r^2 }$$

e.mccormick · Answer

Hehe.