168k views
5 votes
A rectangular box is designed to have a square base and an open top. The volume is to be 2048in.3

What is the minimum surface area that such a box can have?

User PSL
by
8.2k points

2 Answers

0 votes

Answer:

hi

Explanation:

Let x = the length of the sides of the base and h = the height:

Volume = (area of base)(height)

V = x2h

2048 = x2h

2048/x2 = h

Surface Area = area of base + 4(area of vertical side)

SA = x2 + 4xh

Eliminate the h by using 2048/x2 = h:

SA = x2 + 4x(2048/x2)

SA = x2 + 8192 x-1

Take the derivative of SA wrt x, set it to zero, solve for x. Plug that value of x into the surface area equation to find the minimum surface area.

User AbaEesa
by
7.9k points
7 votes

Answer:

x=y=z in 3 dimensions. So, you have x2y=4=x3⟹x=y=3√4.

Explanation:

User Amadou Kone
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories