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 =