00:01
Hello everyone, in this problem we are given with the volume of the rectangular open box is given as, volume will be given by the formula length, breadth and height.
00:17
So, its value is given as 364 .5 meter cube.
00:24
So, now we need to find the minimum surface area.
00:27
So, to have the minimum surface area, now let us take the length l to be equal to the breadth b.
00:40
So, therefore, the volume equation will become, volume will become l square h.
00:48
So, l square h will have the value of 364 .5.
00:53
So, from this we get the value of height to be 364 .5 divided by l square.
01:02
So, in order to find the minimum surface area, so first we need to find the surface area of the open box.
01:11
So, the surface area of the box will be given by the formula l, sorry, length into breadth plus 2 times of length plus breadth multiplied by height.
01:35
So, here we have taken the value of l to be equal to b.
01:39
So, applying the value of l to be equal to b.
01:42
So, we have this value to be, so the surface area a will become l square plus 2 of 2l and substituting the height value here, so it will be 364 .5 divided by l square.
02:04
So, simplifying this we have the area to be equal to l square plus 1458 divided by l.
02:14
So, let us take this to be equation number 1.
02:17
So, now, as we need to find the minimum surface area, so in order to find the minima or maxima, we need to take the first derivative of the area and we need to equate that to 0...
