- #1

- 29

- 0

## Main Question or Discussion Point

"Hi, I have a question on max vol. q. Its invloved with multivariable calculus.

Q) Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9x^2+36y^2 + 4z^2 = 36.

What i did was i found the three x,y and z-intersection points.

(2,0,0), (0,1,0), and (0,0,3)

Then, I just assumed the following equation:

(2x)/4 + y +(3z)/9 = 1. <- I substituted value of x,y and z for the intersection value.

And if i simplify it, i get: z = 3 - 3x/4 - 3y

To find volume,

V = xyz

so,

V = xy(3 - 3x/4 - 3y)

and fsubx = 3y-3xy-3y^2 = 0

fsuby = 3x - (3x^2)/2 -6xy = 0.

If i do the calculation

i get: 6y - 3x -3y^2 +3(x^2)/2 = 0.

and x = 2/3 and y = 1/3.

And if i sub 2/3 and 1/3 for x and y in the original equation, i get

V = 2/9.

IS THIS THE RIGHT WAY TO DO IT? I ASSUMED THE BEGINNING PART OF THE PROBLEM SOLVING SO I MIGHT BE COMPLETELY WRONG. ANY OF YOU MATH EXPERT, PLEASE HELP ME OUT!!!! THANK YOU SO MUCH AND HAVE A NICE DAY!!!

(PLEASE PROVIDE ME THE COMPLETE ANSWER AND EXPLANATION ON THE QUETSION.)

AGAIN THANK YOU SO MUCH!!!

Q) Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9x^2+36y^2 + 4z^2 = 36.

What i did was i found the three x,y and z-intersection points.

(2,0,0), (0,1,0), and (0,0,3)

Then, I just assumed the following equation:

(2x)/4 + y +(3z)/9 = 1. <- I substituted value of x,y and z for the intersection value.

And if i simplify it, i get: z = 3 - 3x/4 - 3y

To find volume,

V = xyz

so,

V = xy(3 - 3x/4 - 3y)

and fsubx = 3y-3xy-3y^2 = 0

fsuby = 3x - (3x^2)/2 -6xy = 0.

If i do the calculation

i get: 6y - 3x -3y^2 +3(x^2)/2 = 0.

and x = 2/3 and y = 1/3.

And if i sub 2/3 and 1/3 for x and y in the original equation, i get

V = 2/9.

IS THIS THE RIGHT WAY TO DO IT? I ASSUMED THE BEGINNING PART OF THE PROBLEM SOLVING SO I MIGHT BE COMPLETELY WRONG. ANY OF YOU MATH EXPERT, PLEASE HELP ME OUT!!!! THANK YOU SO MUCH AND HAVE A NICE DAY!!!

(PLEASE PROVIDE ME THE COMPLETE ANSWER AND EXPLANATION ON THE QUETSION.)

AGAIN THANK YOU SO MUCH!!!