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

hello stranger let's start in this video we are going to talk about the

effect

of increasing the length of the sides of a box on its capacity or

volume

so the question is if it doubles the length of the sides of a rectangular prism which is a box, how many times the

volume

of the old box will be the

volume

of the new box? So, to give you an idea, this is the size of my original box if I double the

dimensions

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

doubled

so we end up with four times the capacity and still haven't

doubled

the height now

when

I double the height everything doubles so it's like adding four more boxes on top actually

when

we double the length of each dimension and width and height w we actually end up with eight times the capacity it also makes sense if you think about the

volume

formula because in our

volume

formula let's assume we have a box that has a length, a width and a height of just one, so the

volume

would be one times one times one we would have a

volume

of one cubic unit if we

doubled

each side then what happens is we're going to have 2 times 2 times 2 which is 8 or 8 times more big will have 8 times e l capacity, let's look at a specific example, here is a box that has a length of 7 inches, a width of 2 inches, and a height of 3 inches, so the

volume

of this box, based on the length times the width times the height , it will be 7 x two by three which will be 42 cubic inches now let's imagine doubling the length of each 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 box bigger will be 14 times? 4 times 6 which turns out to be 336 cubic inches to see how many times bigger than 42, that is, dividing 336 divided by 42 gives us eight, so it is eight times the