A closed rectangular storage container of width x metres...

Name: a closed rectangular storage container of width x metres length 2x metres and height y metres is to be constructed in such a way that its total surface area is 16875 m2 2x y x determine the 40298
Uploaded: 2022-06-21T18:18:30-08:00
Duration: 5 min 40 s
Channel: William Semus
Description: a closed rectangular storage container of width x metres length 2x metres and height y metres is to be constructed in such a way that its total surface area is 16875 m2 2x y x determine the 40298

A closed rectangular storage container of width $x$ metres, length $2x$ metres and height $y$ metres is to be constructed in such a way that its total surface area is $168.75$ m$^2$. $2x$ $y$ $x$ Determine the value of $x$ which will give the largest possible volume of such a container.

Transcript

00:01 So in this question, we say that a hollow, closed, rectangular tank is made from sheet metal of negligible thickness.

00:09 The tank has a length of 2x meters, a width of x meters, and a total external surface area of 48 square meters.

00:18 I want to express, in terms of x, the height of the tank, and the volume of the tank.

00:24 Then, given that x can vary, we're going to find the dimensions of the tank for which the volume is, is a maximum.

00:32 So what do i know about the surface area of a rectangular box? i know that it's two times the length times the width plus two times the height plus two times the width times the height.

00:51 That's my formula for the surface area of a box.

00:55 Now they said that my length this time is 2x.

01:04 My width is x.

01:07 My length is 2x again.

01:13 My height is h.

01:16 My width is x.

01:20 Now my surface area is supposed to be 48.

01:25 So i now know that 48 is equal to 4x squared plus 4xxx plus 4x plus 2xh, or equivalently, 48 is equal to 4x squared plus 6x.

01:46 Now, i want to solve for the h for the height of the tank.

01:54 So what do i know? well, i can subtract 4x squared from each side.

01:59 I can say 6xh is equal to 48 minus 4x squared.

02:08 And if i divide by 6x, my h is equal to 48 minus 4x squared being divided by 6x.