# A box, open at the top is to be made from cardboard. The base of the box is a square of side x and its height is y. If the volume of the box is 32u^2, find the dimensions of the box if the area is to be least. Please help?

##### 2 Answers

See the explanation please.

#### Explanation:

The indicated volume does not make any sense and needs to be

clarified, but for now we can assume the volume to be

The area of the base is:

The volume would be:

Calculating

Total surface area of a box with open top is:

Substituting for

To find the critical points equate the first derivative to zero:

To verify the nature of the critical point use 2nd derivative test:

Thus the box dimensions for a minimum surface area are:

And the minimum surface area would be:

#### Explanation:

Assuming the units expressed for the volume are correct and are indeed expressed in terms of

Volume

From ....

Differentiating ......

The second derivative =