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### Course: 6th grade > Unit 10

Lesson 3: Volume with fractions- Volume of a rectangular prism: fractional dimensions
- Volume by multiplying area of base times height
- Volume with fractions
- How volume changes from changing dimensions
- Volume of a rectangular prism: word problem
- Volume word problems: fractions & decimals

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# How volume changes from changing dimensions

In geometry, altering the dimensions of a rectangular prism impacts its volume. If you double one dimension, the volume doubles. If you double two dimensions, the volume quadruples. When all dimensions are doubled, the volume increases eight times. This is a fundamental concept in understanding volume.

## Want to join the conversation?

- Could you make a video on changing dimensions, but this time could you talk about changing dimensions but still getting the same volume?(49 votes)
- I think this is covered under surface area section.(36 votes)

- When volume remains constant what is the impact on the surface area of a rectangular prism of a change in the dimensions(27 votes)
- Surface area and volume are not the same. You may want to check out the surface area section. But, if you maintain volume, and change one dimension, you will have to either increase or decrease another dimension to make this happen.(20 votes)

- So, in school we are learning about change in dimensions and my teacher makes it so confusing with a whole bunch of formulas like new area over old area and I just don't get it can someone explain it for me in a more simpler way?(14 votes)
- If you double one of the dimensions, say change one side from 2 to 4 it doubles the volume. if you were to do this to any side, say double it, it would double the volume. The box was 2x3x5. If you double any of those numbers, it doubles the volume. A 2x3x5 box has a volume of 30. If you doubled the 2 to a 4 making it a 4x3x5 box, the volume becomes 60. Lets say you changed the one side from 5 to 10 making it a 2x3x10 box, same thing , volume goes from 30 to sixty. Lets say you changed the one side from 2 to 8, essentially 4 times its original length. now the box is 8x3x5. It will make the volume 4 times as much also. the volume would go from 30 to 120. hope this helps. :)(27 votes)

- you said this at the one minuet and eight second in the video why does the three stay the same?(20 votes)
- 4:10it will be multiplied by 8(10 votes)
- Yes it is cause 2*2*2 =8(5 votes)

- Why do the call it 3D I mean if there is a 3rd Dimension there has to be millons ands millons more demensions right?(5 votes)
- ummm. we live in a 3D world. there is a 4th dimention which is time.

the string theory, however, suggests that there are 10, 11 or even 26 dimensions. but so far, it hasn't been prooved.(12 votes)

- Any chance the video could finish the information presented?

Leaving off the answer & its description was completely unhelpful. Sal asked a question, but never provided the information after4:13. I am disappointed.(9 votes) - In Quiz 1 There's a question I don't understand. They said to solve h in (20m x 50m x h = 3000 m^3) How do i find "h"?(4 votes)
- Since you asked this question a few months ago, you've probably already figured it out by now. However, I will still provide an answer in case anyone else has the same question.

It's not stated but from your question, I'm assuming the figure for which you're solving the volume for is a rectangular prism, which has a volume formula of length * width * height (equivalent to lwh) = volume. We can then substitute the given information into the formula, getting 20m * 50m * h = 3000m^3. We can now use equivalence-preserving operations on both sides of the equation to solve for h.

First, I would simplify the left hand side to get 1000m^2 * h = 3000m^3. I would then divide both sides of the equation by 1000m^2 to get h = 3m. Hope this helps!(7 votes)

- How would you measure the volume of shapes like cones, cylinders, or pyramids?(4 votes)
- The volume of a cone with radius r and perpendicular height h is given by V = (1/3)pi r^2 h.

The volume of a cylinder with radius r and perpendicular height h is given by V = pi r^2 h.

The volume of a pyramid with base area A and perpendicular height h is given by V = (1/3)Ah.

(Note that a cone can be thought of as a pyramid with a circular base, so in the formula for the volume of a cone, pi r^2 is used in the place of A.)

Have a blessed, wonderful day!(3 votes)

- My FLVS flex geometry honors class brought me here.(5 votes)

## Video transcript

- [Narrator] I have a
rectangular prism here and we're given two of the dimensions. The width is 2, the depth is 3. And this height here, we're
just representing with an H. And what we're gonna do in
this video is think about how does the volume of this
rectangular prism change as we change the height? So let's make a little table here. So let me make my table. So this is going to be our height and this is going to be
our volume, V for volume. And so let's say that the height is 5. What is the volume going to be? Pause this video and see
if you can figure it out. Well, the volume is just going
to be the base times height, times depth, or you
could say it's gonna be the area of the square. So it's the width times the depth, which is 6 times the height. So that would be 2 times 3 times 5, so 2 times 3 times 5, which
is equal to 6 times 5, which is equal to 30, 30 cubic units. We're assuming that these
are given in some units, so this would be the units cubed. All right, now let's think about it if we were to double the height, what is going to happen to our volume? So if we double the height, our height is 10, what is the volume? Pause this video and see
if you can figure it out. Well, in this situation we're
still gonna have 2 times 3, 2 times 3 times our new height, times 10. So now, it's going to be 6
times 10, which is equal to 60. Notice when we doubled the height, if we just double one dimension, we are going to double the volume. Let's see if that holds up. Let's double it again. So what happens when
our height is 20 units? Well, here our volume is
still gonna be 2 times 3 times 20, 2 times 3 times 20, which is equal to 6 times
20, which is equal to 120. So once again, if you double
one of the dimensions, in this case, the height,
it doubles the volume. And you could think of it the other way. If you were to halve, if you
were to go from 20 to 10. So if you halve one of the
dimensions, it halves the volume, you go from 120 to 60. Now, let's think about
something interesting. Let's think about what happens if we double two of the dimensions. So let's say, so we know, I'll
just draw these really fast. We know that if we have a situation where we have 2 by 3 and this height is 5, we know the volume here
is 30, 30 cubic units. But now let's double
two of the dimensions. Let's make this into a 10
and let's make this into a 4. So it's gonna look like this, and then this is gonna be a 4. This is still going to be a 3, and our height is going to be a 10. So it's gonna look something like this. So our height is going to be a 10. I haven't drawn it perfectly to scale, but hopefully, you get the idea. So this is our height at 10. What is the volume gonna be now? Pause this video and see
if you can figure it out. Well, 4 times 3 is 12 times 10 is 120. So notice when we doubled
two of the dimensions, we actually quadrupled. We actually quadrupled our total volume. Think about, pause this video and think about why did that happen? Well, if you double one
dimension, you double the volume, but here we're doubling one dimension and then another dimension. So you are multiplying by 2 twice. So think about what would happen if we doubled all of the dimensions. How much would that increase the volume? Pause the video and see if
you can do that on your own. In general, if you double
all the dimensions, what does that do to the volume? Or if you halve all of the dimensions, what does that do to the volume?