00:01
In this question, we are given a rectangular box without an open for which we have to find the total area.
00:10
So the total area from the picture is xy plus 2y is it plus 2 is it x because it is open at the top.
00:26
So we are asked to calculate m of x comma y comma z which is the total area xy plus 2y is it.
00:36
Plus 2 x x but x is equals to 9 y is equals to 11 and z is equals to 5 so we have m of 9 comma 11 5 which is equals to 9 multiplied by 11 plus 2 multiplied by 11 multiplied by 5 plus 2 multiplied by 5 plus 2 multiplied by 5 is 110 plus 90.
01:10
So we get 299 square inches, which is the required area.
01:21
Next subdivision, we have volume, which is given as 780 cubic inches, and we have to find the dimensions.
01:37
We have also given some of the readings, x y z is equal to 780 so this can be returned as is it is equals to 780 over xy so let us substitute this in the first equation that is the main equation so we get let us keep that as s xy plus 2y of z which is 780 over xy plus 2 of z squared 780 over x y multiplied by x so we get s is equal xy plus 2 multiplied by 6x because here y and y, here x and x gets cancelled.
02:49
So we are left with this terms.
02:52
So after this, multiplying we get s is equals to xy plus 1560 over x plus 1560 over y.
03:04
So d s over d x is equals to y subtracted by 1560 over x squared and...