From a rectangular peice of cardboard having dimensions 20 inches x 30 inches, an open box is to be made by removing squares of area x^2 from each corner and turning up the sides.
(a) Show that there are two boxes that have a volume of 1000 in^3.
(b) Which box has the smaller surface area?
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constructing a box from cardboard rect. 20 in by 30 in 
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constructing a box from cardboard rect. 20 in by 30 in
by princesscut on Mon Nov 09, 2009 8:54 am
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by stapel_eliz on Mon Nov 09, 2009 11:46 am
You can review the general set-up on this page.
To find the solutions, you'll need to solve the equation that results from setting the "volume" expression (20 - 2x)(30 - 2x)(x) equal to the given volume value. I don't know what techniques they've given you for solving cubics, though...?
To find the surface areas, it might be helpful to draw a picture, so you can more-easily "see" what are the expressions for the areas of each side. Plug in the values you got for "x" in part (a), and see which situation gives you the smaller value.
If you get stuck, please reply showing how far you have gotten. Thank you!
To find the solutions, you'll need to solve the equation that results from setting the "volume" expression (20 - 2x)(30 - 2x)(x) equal to the given volume value. I don't know what techniques they've given you for solving cubics, though...?
To find the surface areas, it might be helpful to draw a picture, so you can more-easily "see" what are the expressions for the areas of each side. Plug in the values you got for "x" in part (a), and see which situation gives you the smaller value.
If you get stuck, please reply showing how far you have gotten. Thank you!
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stapel_eliz - Posts: 1264
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