Find the height of a cylinder with radius 13 and surface area 1470.3.

Question

whpalmer4 · Answer

surface area of a cylinder is the surface area of the top + surface area of the bottom plus surface area of the side.  

top and bottom are both just circles, so their areas are $$A = \pi r^2$$ and because you have two of them, the total area of top and bottom is $$A = 2\pi r^2$$

The side is a rectangle rolled up so the edges meet.  The length is the height of the cylinder $(h)$, and the width is the circumference of the cylinder, $2\pi r$, so the area of the side is

 $A = \ell * w = h * 2\pi r = 2\pi r h$

Adding the two together, we have the surface area of the cylinder:
$$A = 2\pi r^2 + 2\pi r h$$

Now you know the surface area and radius, and want to find its height.  Solve the surface area equation for $h$ and plug in the numbers.

anonymous · Answer

omg I cant do it i hate math!! what would it be?

whpalmer4 · Answer

$$A = 2\pi r^2 + 2\pi r h$$Subtract $2\pi r^2$ from both sides, and what do you get?

anonymous · Answer

umm idk

anonymous · Answer

I know that its either 3 4 5 or 6 but I cant doo itt

whpalmer4 · Answer

Okay, let's say we have a different equation.

5 = 2 + 3

what do you get if you subtract 2 from each side?

anonymous · Answer

3=3

whpalmer4 · Answer

well, before that, you get 

5-2 = 2 + 3 - 2

right?

anonymous · Answer

yes

whpalmer4 · Answer

okay, well, do the same thing with that equation!

$$A = 2\pi r^2 + 2 \pi r h$$subtract $2\pi r^2$ from each side, and you get?

whpalmer4 · Answer

$$A - 2\pi r^2 = \cancel{2 \pi r^2} + 2 \pi r h \cancel{- 2 \pi r^2}$$$$A - 2\pi r^2 =  2 \pi r h $$Right?

anonymous · Answer

yeah I think

whpalmer4 · Answer

Look, if that isn't crystal clear to you, you need to talk to your teacher immediately and have them help you until it is.  This is really basic, and if you don't have a good handle on it, you won't do well...

Bottom line: you can do just about anything to one side of the equation as long as you also do it to the other side.  We subtracted the same thing from both sides, and so the equation remains true.

Okay, we want to get $h$ all by itself ("subject of a number sentence as some people put it"), with everything else on the other side of the equals sign.  We still have $h$ being multiplied by $2\pi r$.  The way to undo multiplication is to divide.  So, what do you get if you divide both sides of the equation by $2 \pi r$?

whpalmer4 · Answer

you'll get $h$ all by itself on one side, but what is the expression on the other side going to be?

anonymous · Answer

ok umm so will the answer be 5?

whpalmer4 · Answer

I don't know, did you punch all of the numbers into a calculator and get that as a result?  what did you use for the formula?