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crenshawalc · Mar 1, 2007, 07:39 PM

How do I figure out the following question:

A close rectangular box has a surface area of 1000 square centimeters. Its length is twice its width and its height is 6 times its width, what is the volume?

Capuchin · Mar 2, 2007, 12:39 AM

From your second piece of information

$\frac{1}{2}l = \frac{1}{6}h = w$

From your first information

$2lw + 2hw + 2hl = 1000$

Now using the first equation to convert everythign into w

$2w(2w) + 2w(6w) + 2(2w)(6w) = 1000$

$4w^2 + 12w^2 + 24w^2 = 1000$

$40w^2 = 1000$

Now you can solve for w, then you can use the first equation I stated to get the length and height.

Then use:

$V = lhw$

to find your final volume.

Let me know if you need more help.