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    A square side x cm is cut from the corners of a piece of card 15cm by 24cm. The card is then folded to form an open box

    i) Show that the volume of the box is 4x3-78x2+360x
    ii) Find a value for x that will make the volume a maximum
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    (Original post by basketballgirl11)
    A square side x cm is cut from the corners of a piece of card 15cm by 24cm. The card is then folded to form an open box

    i) Show that the volume of the box is 4x3-78x2+360x
    ii) Find a value for x that will make the volume a maximum

    Name:  Capture.PNG
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    You have a rectangle of length 24cm by 15cm. At each corner a square of length x is cut. So then visualise this box and derive the volume.
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    (Original post by basketballgirl11)
    A square side x cm is cut from the corners of a piece of card 15cm by 24cm. The card is then folded to form an open box

    i) Show that the volume of the box is 4x3-78x2+360x
    ii) Find a value for x that will make the volume a maximum
    The red area is cut out and then folded along the dotted lines to make a box:



    Does that help?
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    I know which diagram I prefer!
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    (Original post by Mr M)
    I know which diagram I prefer!


    Well as long as the main idea is understood... :lol:
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    (Original post by notnek)
    The red area is cut out and then folded along the dotted lines to make a box:



    Does that help?

    it does help yes, just dont know how to show the volume now
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    (Original post by basketballgirl11)
    it does help yes, just dont know how to show the volume now
    If you want a 3d image then that might be beyond my talents

    If you can picture the box in 3d, think about what the length, width and height are. Post your thoughts if you're not sure.
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    (Original post by basketballgirl11)
    it does help yes, just dont know how to show the volume now
    You know how to find the volume of a cuboid. What are the three measurements you need to use here?
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    (Original post by notnek)
    If you want a 3d image then that might be beyond my talents

    If you can picture the box in 3d, think about what the length, width and height are. Post your thoughts if you're not sure.
    I was thinking that as a 2D shape the width would be 24 - 2x as the corners are cut off and the length is 15 - 2x but somehow i have to prove the volume is the equation i mentioned previously
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    (Original post by basketballgirl11)
    it does help yes, just dont know how to show the volume now
    Well, we know that the length of the short side will be using the 15 CM and the fact that 2X is removed from it, and we know the longer side was 24 CM long and had 2 X removed from it. Then it's just like calculating the volume of any old cuboid
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    (Original post by Callicious)
    Well, we know that the length of the short side will be using the 15 CM and the fact that 2X is removed from it, and we know the longer side was 24 CM long and had 2 X removed from it. Then it's just like calculating the volume of any old cuboid
    i've got it now, thank you
 
 
 
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