Question

I really don't understand this dimension changing thing... Can someone please help me understand this?
If all the dimensions of a cylinder are doubled, the volume of the cylinder will be quadrupled.


True or False

Answer 1

by dimension, they mean height, width and length.

If a volume (of any shape) has each of its height, width and length doubled, the volume will go up by 2*2*2= 8 times. quadrupled means 4 times.

Answer 2

oh so for this that would be true?

Answer 3

If you multiply each dimension by 2, what do you end up multiplying the volume by ? (see above post)

Answer 4

2*2=4 if it's doubled

Answer 5

If a volume (of any shape) has each of its height, width and length doubled, the volume will go up by 2*2*2= 8 times

Answer 6

It might be more obvious for a cube.

volume of a cube is L*W*H but length, width and height are all the same number. call it L
V= L*L*L
if we double each dimension to 2L, the new volume is
2L*2L*2L= 8*L*L*L= 8 * old volume

Answer 7

Another way of seeing it: imagine you have a shape that is a brick. Volume of the brick is length * width * height. \(V_{old} = l*w*h\)

Now you make another brick, with each dimension being 2x that of the old brick. The formula is still the same, but here we'll have \[V_{new} = (2l)*(2w)*(2h) = 8lwh\]

If we divide the new by the old, \[\frac{V_{new}}{V_{old}} = \frac{8lwh}{lwh} = 8\]

So we can see that just need to plug in the scale factors of every dimension in the formula

Answer 8

And if we only changed some of the dimensions, this works also. For example, say we made our brick twice as long, but kept the other two dimensions constant, we would have lwh = 2*1*1 = 2 so 2x the volume.

I find the most useful application of this is when deciding whether or not to buy the really big pizza :-)

Answer 9

Hmm @phi well for some reason my math teacher said, if it says to double a number it =the number x 2x2=4 so 4x that number... But I guess she was wrong.
So it's 2*2*2=8 times. And thats all the steps?
@whpalmer4 Oh I see that makes good sense... :)

Answer 10

It's possible you misheard what your teacher said, too.

Answer 11

well I typed it out in my notes what she had up on the paper... Oh well, maybe I read it wrong. :P

Answer 12

ask your teacher again, but I think she means
doubling x means 2x

doubling each dimension means 2 times each: length, width and height.

btw, if they ask about surface area, doubling each dimension makes the surface area of the shape by 4 times.

Answer 13

but to finish this question, quadruple does not mean 8 times (it means 4 times)

Answer 14

For proof that your teacher means 2x when she says doubling, give her a dollar, ask her to double it, observe whether she gives you 2 or 4 dollars in return :-)

Answer 15

okay so I found the answer :) it's actually tripled

Answer 16

And you both gave so great of help that I don't know who to give the medal to :P so I'll just have to fan you both! :)

Answer 17

No, it's not. If you double all the dimensions of a cylinder, the volume goes up by 8.

Volume of a cylinder with height 1 and width/length = 1 is
\[V = \pi r^2h = \pi(1/2)^2(1) = \pi/4\]
Volume of a cylinder with height 2 and width/length = 2 is
\[V=\pi r^2h = \pi(1)^22 = 2\pi\]\[\frac{2\pi}{\pi/4} = 8\]

Answer 18

oh hmm, I see... so you're saying it goes up by 8?

Answer 19

Look, you know it has to double just from doubling the height. To only triple overall after you've doubled, means that doubling the size of the base only increases the area of the base by 1.5. That's not true — think of a square. Double the side of the square, the area goes up by 4. A circle does the same thing, in proportion.

Answer 20

Yes, the answer is 8.

Answer 21

Oh I see, I think I get it now. Thanks :)

Answer 22

Good!