# Dimensions of box with largest volume

by evilpostingmong
Tags: dimensions, largest, volume
 P: 341 1. The problem statement, all variables and given/known data Find the dimensions of a rectangular box with the largest volume with surface area 64cm^2. 2. Relevant equations area of a rectangular prism 2xy+2yz+2xz 3. The attempt at a solution took 2xy+2yz+2xz=64 rearranging for z: z=(xy-32)/(y+x) partial derivative of z with respect to x y/(y+x)-(xy-32)/(y+x)^2 partial derivative of z with respect to y x/(y+x) -(xy-32)/(y+x)^2 setting both derivatives equal to zero to obtain the critical point.... Here's where I hit a wall- I cannot get a real root for y. y/(y+x)-(xy-32)/(y+x)^2 y^2+xy=xy-32 y^2=-32 Please only help me up to this point until I ask you to help me further, I want to challenge myself. Thank you!
 P: 2,258 what are you maximizing?
 P: 341 The volume of this box.
P: 2,258

## Dimensions of box with largest volume

you're maximizing xyz?
 P: 341 Oh wait I'm finding the maximum dimensions that can be used to get the surface area of 64cm^2. So I maximize 2xy+2yz+2xz=64
 P: 2,258 'maximum dimensions'?
 P: 341 The problem states that I must find the dimensions of a rectangular box with the largest volume if it's total surface area is 64cm^2. What we don't know is how long those dimensions are.
 P: 2,258 first you should find the maximum volume of a box with surface area 64cm^2.
 P: 341 Okay! I'll take the problem from there and tell you how I made out.

 Related Discussions Precalculus Mathematics Homework 6 Precalculus Mathematics Homework 5 Calculus & Beyond Homework 3 Introductory Physics Homework 2 General Physics 7