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A fruit crate has square ends and is twice as long as it is wide.

a. Find the volume of the crate if its width is 20 in.

b. Find a formula for the volume $V$ of the crate in terms of its width $x$

a.$=16000$

b. $V=2 x^{3}$

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{'transcript': "So in the top left corner over here, I have copied diagram for more book, which lists the dimensions of this rectangular crate. So are with here is X Our height is X and our length is too x. And the way that we find the volume of any rectangular prism such as this one, is we're going to multiply the three dimensions. So the with the height and the like, so we're given the with X is 20 inches. And we know that since this one base is a square, the height is also 20 inches and we're told that the length is too. Times are with, so it's going to be two times 20 inches, which is equal to 40 inches. So our volume is equal to our ex from right here. So 20 times are extreme. Right Here is another 20 times are two ex length, so that'll be times two times 20. So we're just going to multiply this all out, so our volume is equal to 400. We're playing these two parts right here at times 40 multiplying these two parts and we get for part a our volume of a box with a width of 20 inches is 16,000 moving on to part beef of over here, we're asked, you find the formula for the volume of the box of the crate that has some with X. So this time we're going to basically create a model with two variables. And we know that we want volume to be all by itself on the left side because it's asking for the formula of the volume. And so, like in for a wee said that we're going to we'll supply the base times the width time seat length for lifetimes, with times height. Excuse me and that's going to give us the volume. So using exes are variable. We're essentially just going. Teo, copy the variables. The dimensions from over in the picture. So our volume is equal to the with which is eggs right down there. Times are height, which is also eggs. Times are length, which is given to us by two ex. So here are formula for volume is equal to to execute"}

University of California, Berkeley

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