💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# If $1200 cm^2$ of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

## 4000 $\mathrm{cm}^{3}$

Derivatives

Differentiation

Volume

### Discussion

You must be signed in to discuss.
##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp

### Video Transcript

Okay. We know the amount of material 1200 can be set equal to X squared. Remember, the boxes has an open top was for X y, and then veer Volume is gonna be X squared Y. So now, writing this first part in terms of why Rise 1200 minus x squared over four ax, which simplifies to 300 over axe minus X over four. Substituting into the equation, we have V is X squared times 300 over. Axe minus X, divided by four. Okay, now that we've got that we know we can differentiate the air volume to get 300 minus three x squared, divided by four. Set this equal to zero. So when we end up with X is a square to 400 which is 20 centimeters. Therefore, we know plugging this end v of 20 is gonna be 300 times 20 minus 20 cubed over four, which is for 1000 centimeters cute for volume.

#### Topics

Derivatives

Differentiation

Volume

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp