Geometry Part 26 Effect on Volume of a Box when Dimensions are Doubled or Tripled

Hello, I'm missing, let's start in this video. We're going to talk about the

effect

of lengthening the sides of a box on its capacity or

volume

. So the question is, if you double the length of the sides of a rectangular prism, that is a box, how many times larger than the

volume

of the old box will be the

volume

of the new box. To give you an image here, this is my original box size, if I double the

dimensions

in each direction, length, width and height it's like I have twice as many boxes in that direction, so if I double the length for example , it's like I put another box on the other side on the right, but that's just one dimension, so what if I double the width as well, now the length and width were

doubled

, so we end up with four times have that much capacity and I still haven't even

doubled

the height, now if I double the height it doubles the whole thing, so that's like we add four more boxes on top, so actually if we each dimension length double and width and height w we end up with eight times the capacity, which also kind of makes sense

when

you think about the

volume

formula, because in our

volume

formula we're assuming we have a box with a length, width and height of only one, so the

volume

would be one by one by one, we'd only have a

volume

of one cubic unit, if we double each side, which happens we'll have 2 by 2 by 2 , which is 8 or 8 times the size that it is 8 times the size Let's look at a concrete example.

Here is a box that is 7 inches long, 2 inches wide, and 3 inches high, so the

volume

of this box is length times width times height 7 x two times three. That will be 42 cubic inches. Now let's imagine doubling the length of each individual edge in each dimension, what if we had a box that was 14 inches by 4 inches by 6 inches, so the

volume

of this new larger box would be 14 times that is 4 times 6, which turns out to be 336 cubic inches, let's see how many times greater than 42, that is, dividing 336 divided by 42 gives eight, so it's eight times the

volume

, and something similar will happen if you use each of

dimensions

would triple how much times the capacity you think you would get.

So remember to go back to the situation where we all have our

dimensions

. We have a cubic unit. If we triple each of these

dimensions

, we get 3 times 3 times 3 is 27 times the capacity. I hope you found this video helpful, if you did please give it a thumbs up it helps other students find the video