Question

So, I was trying to find the radius of a cylinder and a question popped up in my head.
IS VOLUME AND DIAMETER THE SAME THING?

Answer 1

I feel like it's not but if the way its set up like this ^

Answer 2

it confuses me

Answer 3

I see! So to understand this thing, you've probably heard for rectangles and cubes and squares that:

Area = length*width
Volume = length*width*height

or shortened,

A=lw
V=lwh

Looks familiar?

Answer 4

yes.

Answer 5

Well, since A=lw and lw is part of the volume formula, we can replace it in there like this:

\[V=lwh = Ah\]

Kinda tricky, so now as long as we know the area of any shape with a height, we can find its volume! So a cylinder has a circle area and a height for instance. So since you know the area of a circle is \(A=\pi r^2\) you can plug this in even further:

\[V = Ah = \pi r^2 h\]

Now you have that equation,

\[V=\pi r^2h\]
you can divide both sides by \(\pi\) and \(h\) and then take the square root, and that's really where this equation comes from:

\[r = \sqrt{\frac{V}{\pi h}}\]

Answer 6

Oh, but that's not how to find the radius?

Answer 7

It isn't? The radius r is right there

For a circle remember \(A=\pi r^2\) so Area = \(\pi\)* radius squared

Answer 8

what about v= 1/3? My math teacher said that, that formula can only help me with cones? True?

Answer 9

It's similar but not the same, the volume of a cylinder is:

\[V = \pi r^2 h\]

The volume of a cone is:

\[V = \frac{1}{3} \pi r^2h\]

and the volume of a sphere is pretty similar so I'll just say it now so you don't confuse it later:

\[V = \frac{4}{3} \pi r^3\]

All of these things are pretty similar cause they all are sorta round in shape.

It should also make some sense that you can fit a cone inside a cylinder so the volume of a cone is a third of the volume of a cylinder!

Answer 10

Oh, okay. :) Thanks. I understand now.

Answer 11

Cool glad I could help :)