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# A Level Differentiation question! Watch

1. Hi,
I'm struggling with this question and I have no idea where to start!

An open box is made from a rectangular piece of cardboard measuring 16 cm by 10cm. Four equal squares are to be cut from each corner and flaps folded up.
Find the length of the side of the square which makes the volume of the box as large as possible.
Find the largest volume.

Thank you
2. You know that the forumla for the volume V of a (box? cuboid? whatever) is simply L*W*H
Find a way of expressing the length and width of the box in terms of the measurements you're given and H, to get an equation for V in terms of h, and then maximise.
3. (Original post by Annabel_lear)
Hi,
I'm struggling with this question and I have no idea where to start!

An open box is made from a rectangular piece of cardboard measuring 16 cm by 10cm. Four equal squares are to be cut from each corner and flaps folded up.
Find the length of the side of the square which makes the volume of the box as large as possible.
Find the largest volume.

Thank you
This diagram may help:

The net is folded along the dotted lines to make a box and x is the length of the square cut offs. What's the volume of the box in terms of x?

Edit My drawing is slightly confusing: The centre rectangles on either side are not necessarily the same size as the four cut-off squares.
4. once you have the Volume, you differentiate, equate to zero, and solve - then examine whether each root gives a maximum volume (except x=0) - no box!
5. (Original post by notnek)
This diagram may help:

The net is folded along the dotted lines to make a box and x is the length of the square cut offs. What's the volume of the box in terms of x?

Edit My drawing is slightly confusing: The centre rectangles on either side are not necessarily the same size as the four cut-off squares.

Would it be:
(16-2x) x (10-2x) x X
6. (Original post by Hasufel)
once you have the Volume, you differentiate, equate to zero, and solve - then examine whether each root gives a maximum (except x=0) - no box!
I don't think x=0 is a root.
7. (Original post by Annabel_lear)
Would it be:
(16-2x) x (10-2x) x X
That's right. Now you need to find the value of x that makes this expression maximum. So differentiate the expression and set it to 0.
8. (Original post by notnek)
I don't think x=0 is a root.
9. Thank you!
10. (Original post by Hasufel)
once you have the Volume, you differentiate, equate to zero, and solve - then examine whether each root gives a maximum (except x=0) - no box!
Thank youu!

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