Question

If 1200 cm squared of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

thank you

Answer 1

The box will be formed by cutting in each side at the corners for a distance x and folding up the sides to form the box. The depth of the box will be x, the length and width will be 1200-2x. Units are cm.

Volume V=x(1200-2x)(1200-2x)
V=x)1440000-4800x+4x^2)

Answer 2

\[V=4x ^{3}-4800x ^{2}+1440000\]

Answer 3

Differentiate and set to for max min

Answer 4

\[12x ^{2}-9600x=0\]

Answer 5

Solve for x the depth, the sides would be 1200-2x. Now if the material is 1200 sq cm and not a piece that is 1200 x1200 then use sides of 1200^sqrt.

Answer 6

The way I read it, was a piece of material 1200 by 1200

Answer 7

I see where I made a mistake in the multiplying failing to multiplying byx

Answer 8

thank you thank you!

In this question, I'm given the surface area --> 1200 = w^2 + 4 ( h x w )

Answer 9

I apologize if I made the question confusing =(

Answer 10

O.K. I'm sorry. does the problem say you have a square piece of material that is 1200 cm sq?

Answer 11

Yes that is correct. I'm sorry for the confusion

Answer 12

Or is the completed box to have 1200 sq cm of surface area

Answer 13

Hm... let me read again. I'm sorrry!!!

Answer 14

Hm... let me read again. I'm sorrry!!!

Answer 15

if \[1200 cm ^{2 }\] of material is available to make a box with a square base and an open top, find the largest possible volume of the box

Answer 16

I am sorry, but I have to go pick up my car. If the problem is not solved when I get back tonight I will make furthert attempts to help. Thanks for clarify. I think I know what you are to do.

Answer 17

Thank you so much for you help sir!

Answer 18

I'm back. if you have 1200 cm^2 of material then you have a square whose sides are equal to the square root of 1200 or 34.64 cm. The box will be formed by cutting in each side at the corners for a distance x and folding up the sides to form the box. The depth of the box will be x, the length and width will be 34.64-2x. Units are cm.

Answer 19

Volume V=x(34.64-2x)(34.64-2x) V=(x)(1200-138.56x+4x^2)
V=1200x-138.5x^2+4x^3

Answer 20

\[V=4x ^{3}-138.5x ^{2}+1200x\]

Answer 21

Now differentiate and set to zero

Answer 22

\[12x ^{2}-277x+1200=0\]

Answer 23

Now you can use quadratic equation and solve for x which represents the depth and the sides would be 34.64-2x. Good luck