# volume

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• October 28th 2008, 11:31 AM
abey_27
volume
Square corners, with side
x cm, are cut from a square card with side 6 cm.

Then the edges are folded up to make a box.

Show that the volume of the box is
V cm3 where V = 36x – 24x2 + 4x3.

much appreciated
• October 28th 2008, 11:35 AM
earboth
Quote:

Originally Posted by abey_27
Square corners, with side
x cm, are cut from a square card with side 6 cm.

Then the edges are folded up to make a box.

Show that the volume of the box is
V cm3 where V = 36x – 24x2 + 4x3.

much appreciated

The volume is calculated by:

$V = base\ area \cdot height$

With your values you get:

$base\ area = (6-2x)^2, 0\leq x \leq3$

$height = x$

Now plug in the terms into the formula of the volume, expand the brackets and collect like terms.