A manufacturing engineer has been given the job of designing an aluminum container having a square base and rectangular sides to hold screws and nails. It also must be open at the top. The container must use 200 cm² of aluminum, and it must hold as much as possible (i.e., have the greatest possible volume). What dimensions should the container have?

Okay, it's been a weekend so lets re-cap everything we've worked so hard to come up with!

		y
	x

x

First we figured out an expression to find y:

What does x² stand for?

What does 200 – x² stand for?

What does y stand for?

Then we found and graphed a formula for volume:

V = x²

Why did we restrict the x between 0 and ?

The “maximum” occurs at the point (8.16497, 272.166)

What do these two values represent?

What is the height of the maximized container?

Answer this question for:

A manufacturing engineer has been given the job of designing an aluminum container having a square base and rectangular sides to hold screws and nails. It also must be open at the top. The container must use _____ cm² of aluminum, and it must hold as much as possible (i.e., have the greatest possible volume). What dimensions should the container have?

300 cm² of fencing Base dimension______ Height ______

400 cm² of fencing Base dimension______ Height ______

500 cm² of fencing Base dimension______ Height ______

600 cm² of fencing Base dimension______ Height ______

700 cm² of fencing Base dimension______ Height ______

What advice would you give anyone who intends on building a container with a square base and rectangular sides that will have the greatest volume possible?

Make up a problem like this one that has nothing to do with aluminum or screws and nails.