Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

A box with a square base and an open top is being constructed out of a cm2 of material. If the volume of the box is to be maximized, what should the side length of the base be? what should the height of the box be? what is the maximal volume of the box? your answers should be in terms of a.

Sagot :

The maximum volume of the box in terms of A will be √3A/4 -3√3/4 cu cm.

It is given that the box has an open top and a square base.

This implies length = breadth.

Let them be x cm

Now, the area of the box is A sq cm

This means

lb + 2bh + 2lh = A

or, x² + 2xh + 2xh = A

or, 4xh + x² = A

or, h = A/4x - x/4

Now volume (V) = lbh

= x²(A/4x - x/4)

= Ax/4 - x³/4

Now to maximize volume we will first differentiate with respect to x and equate it to zero. Hence we get

V' =0

or, A/4 - 3x²/4 = 0

or 3x²/4 = A/4

or, x² = 3

or, x = √3

Now t check whether this gives us the maximum volume we will calculate V"(√3)

V" = -3x/2

V"(√3) = -3√3/2

Since V"(√3) is negative we will get maximum value for x = √3

Now the volume is

A√3/4 - (√3)³/4

= √3A/4 -3√3/4 cu cm

To know more about maximization visit

https://brainly.com/question/14682292

#SPJ4

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.