ok, we are in section 25 ### effects

of #### changing

the ## dimensions

of the dimension in the ### volume

and let's find the ### volume

of this prison remember that the ### volume

formula is the area of the base times the height and in this, since it is a rectangle, the base is the link times the width so I'm going to change the uppercase B to LW because that's going to be your base area so on this just make the link times the width times the height so it's going to be 5 times 2 times 4 10 and 10 times 4 is 40, so 40 cubic feet would be the ### volume

of this prison, let's see what happens when we change one or both ## dimensions

, let's go ahead and write 40 for our original and then what happens is us. i am going to change some things i am going to make a link that is twice as long a width that is twice as long and a height that is three times as long ok now what is going to happen this time if the length, the width and the height are going to change to double the length for the link which is going to make the link 10 the width is going to be twice the length so it's going to be four and the walk is going to be twice sorry three times as long like this which is going to be 12 so that's 40 times 12 so the ### volume

of the new prison would be 480 cubic feet let's go ahead and finish the graph this column here in this what they want to do they want to change the link three times as long there is no changes here so we'll just say x 1 for the width and twice the length times the height so your length times your width times your height on this your link three times as much as five that's 15 no change in the width so leave a 2 and your height is twice as long so that's going to be 8 so that's going to be 15 times 2's or it is 30 by eight that would be a ### volume

of 240 cubic feet let's talk about the next one the next one that they are going to do the length is going to change four times we are going to multiply the desire half times and we are going to multiply it by three the height so in this your new ### volume

your length 4 times 5 is 20 half your width would be 1 and your walk is three times as big so it would be 12 so that's 20 x 12 so your ### volume

happens to also be 240 cubic feet okay let's look at a pattern here we've done this before with area but let's look at this one the new ### volume

too sorry 80 if we divide it by our original 480 / 4 will give you 12 on this your new one is 240 your original was 40 and 2 40 / 40 it's 6 in the last one that was changed to 40 / 40 which can also be six ok I want you to notice what's going to happen here you take these ## dimensions

and change it to 2 2 & 3 if you multiply this two times two times three see what gives you 12 here three for one times to notice that it gives you six and again four for u n half times three that's going to give you six so this is going to help you when you'll notice that the guess here would be that the new ### volume

is multiplying the original fund by the product of the factors. s write that on the next page tell what guess you can make about the effect of #### changing

the ## dimensions

on the ### volume

and let's write that's ok the ### volume

to get the new ### volume

you multiply the original ### volume

by the product of the factors you are #### changing

the ## dimensions

by ## dimensions

and that's some of what we've noted in the checkout in the chart we just made let's try one suppose the ### volume

of a right triangular prism is 360 cubic units what would its new ### volume

be if one of its ## dimensions

were the twice as long a second dimension was three times as long and a third dimension was half as long note that they are giving you the different changes here let's write down our changes we have one dimension that has changed twice as long and another that has changed three times as long time and then half the time remember it's the product of these factors that you're #### changing

by so if you multiply six by half that gives you day three so you take what your new ### volume

would be what the old ### volume

was the original ### volume

multiplied by the product of the changes so this gives us our new ### volume

so that would be 1080 and cubic units so really just look at the change in all the ## dimensions

and multiply them to find the factor that will make your new year new. ### volume

let's look at example three suppose the ### volume

of a cube is 54 times the square root of three cubic centimeters what would be its new ### volume

if one of the ## dimensions

were halved the second dimension was doubled and a third dimension was unchanged so let's write down the changes again in this the new ### volume

one of its ## dimensions

has the second was doubled and the third was not changed now when it doesn't change remember to put it use factor one when it doesn't change then half times 2 is 1 and 1 times 1 is 1 look at this every time you get a 1 which means no change because multiplying by one you will still be the same so your new ### volume

will be the same as your original it will be 54 times. the square The root of three times yours, which means it will stay at 54 times the square root of three.

I think I'll give you the decimal answer as well. Let's put that into our calculator and see what that would be. This is an exact answer and our estimate is about 93.5 and this is cubic centimeters so we can write it as one centimeter to the power of three and this is how you determine the change in ### volume

when you change something this is how you just take the product of the factors on what you are #### changing

the ## dimensions

well, now it's time to do some work on your

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