Question

What is the height of a cylinder with the volume of 84cm^3 and a radius of 2. And from there, what would be the area of that same cylinder?

Answer 1

The volume of a cylinder is \[H \pi r^{2}\]

You know the volume so you divide that by pi:
84\pi = Hr^2

You know r, so divide Hr^2 by r^2 and you have your height.

Now that you have your height, the area of a cylinder would be pi*2r*H

Answer 2

Thank you. I have the formulas, I just wasn't sure if the answers that I came up with were correct. I got 107.01 for the Height and 2713.2 for the area. ??

Answer 3

No.

First divide your volume by pi.

What does that give you?

Answer 4

26.75?

Answer 5

26.74 to 2 places, actually.
But this number represents your "height * r^2"

You know what your radius is, so what do you get if you divide 26.74 by r^2?

Answer 6

6.685. the formula I found said V/pir^2. Does that change what my answer would have been, or did I just calculate it wrong? I notice that the formula I had for area was also different than what you had... mine was 2pir^2+2pirh

Answer 7

Ah yes...there is an ambiguity here...
My formula pi*2r*H (which is your "2pirh") is for the cylinder wall alone.
If the ends are capped (as in an oil drum or some such) and you want to include those surfaces you have to find the area of a cap with pi*r^2, and then multiply that by the number of caps you have which is 2. So this is where your "2pir^2" came from.
Sorry if I caused any confusion, and I probably should have covered that in the first place.

And getting back to the previous argumen... :-)
Yes, 6.685 is correct to 3 places.
And this number is the height of your cylinder.
You now have all the values you need to find all areas and surfaces:
r = 2
H = 6.685

Answer 8

Are you okay with this now or do you need more help?

Answer 9

I am so sorry, my computer had some sort of meltdown as I was typing my reply back. I think I got it, but I am going to have to come back and make sure tonight. Thank you so much for all of your help!