Question

If the dimensions of a cylinder are doubled, then its volume is quadrupled. Which I know is false.
But my question is what is the dimensions of its volume going to be, doubled? I'm getting ready for my test.

Answer 1

Think of a cylinder with radius = r, and height = h.
What is the volume of that cylinder?

Answer 2

Oh so I have to use pi x r2x h and find the volume?

Answer 3

That is it. Let's just write it as
V = (pi)r^2h

Now you double the dimensions. That means that the radius becomes 2r and the height becomes 2h.
What is the volume of a cylinder with radius 2r and height 2h?

Answer 4

But how are you suppose to find out what r and h is? Because it gives no numbers.

Answer 5

You don't need specific numbers for r and h because you just want a ratio between volumes, and r and h will cancel out. You'll see soon.

What is the volume of a cylinder with radius 2r and height 2h?

Answer 6

so you're saying 2xr and 2xh?

Answer 7

The volume of a cylinder is V = (pi)r^2h, for radius = r and height = h.
Since we want radius = 2r and height = 2h, the volume is:
V = (pi)(2r)^2(2h)

Answer 8

Yes, the height is now 2*h and the radius is now 2*r

Answer 9

V = (pi)(2r)^2(2h) = (pi)(4r^2)(2h) = 8(pi)r^2h
Now notice above that the new volume for the doubled cylinder is 8(pi)r^2h.

The original volume for the cylinder is (pi)r^2h

Divide the new volume by the original volume:
8(pi)r^2h/(pi)r^2h = 8
So the volume is 8 times larger.

Answer 10

oh, I see... that makes better sense. So the volume is 8 times larger than the original volume?

Answer 11

Right. And since when we divided the new bigger volume by the original smaller volume, r and h cancelled out, and all we get is 8, that means that for any cylinder with any radius and height, if you double the radius and the height, you'll make the volume 8 times larger.

Answer 12

Oh okay, wow thanks! :)

Answer 13

You're welcome.