question about maximum volume

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cotfw

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Sep 29, 2014
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I am having some trouble with this one.

"A rectangular sheet of tin, 30 x 24 cm, has four equal squares cut out at the corners, and the sides are then turned up to form a rectangular box. What must be the length of the side of each square cut away, so that the volume of the box may be as great as possible?"

I thought this would be the equation for the volume:

(30 - x)(24 - x)(x) , where x is the length of the squares cut from the corners. That turned into x3 - 54x2+ 720x.

Then I thought I should differentiate this, which ended up being 2x2 - 108x + 720. Then i used the quadratic equation to get the zero values and they ended up being 54 and 0.

The derivative of the derivative ended up being x - 27. After plugging 54 and 0 into this, I found that 0 was the maximum. But this was not the correct answer. Do you know how to do this?

EDIT: Okay i think that i got the zero values wrong, but with the correct zero values, i am still wrong about the final answer.

EDIT 2: Argh okay I think I got the volume equation wrong. it should be (30 - 2x)(24-2x)x i think. i will be back in a second

Edit 3: yes i was right I got it now.
 
Last edited:
cotfw said:
I am having some trouble with this one.

"A rectangular sheet of tin, 30 x 24 cm, has four equal squares cut out at the corners, and the sides are then turned up to form a rectangular box. What must be the length of the side of each square cut away, so that the volume of the box may be as great as possible?"

I thought this would be the equation for the volume:

(30 - x)(24 - x)(x) , where x is the length of the squares cut from the corners. That turned into x3 - 54x2+ 720x.

Then I thought I should differentiate this, which ended up being 2x2 - 108x + 720. Then i used the quadratic equation to get the zero values and they ended up being 54 and 0.

The derivative of the derivative ended up being x - 27. After plugging 54 and 0 into this, I found that 0 was the maximum. But this was not the correct answer. Do you know how to do this?

EDIT: Okay i think that i got the zero values wrong, but with the correct zero values, i am still wrong about the final answer.

EDIT 2: Argh okay I think I got the volume equation wrong. it should be (30 - 2x)(24-2x)x i think. i will be back in a second

Edit 3: yes i was right I got it now.
Click to expand...

I am glad you found the correct solution by yourself. Nice Work...
 
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