Asked by cindy

carl has a box with a length width and height of 12 inches. she needs a box that is 4 inches longer, not as high, yet still has exactly the same width and volume.

what are the new dimensions?
which box requires more material to construct?


PLEASE HELP ME!! :(
Answered by victoria
length would be 16 , width 12, and hight 9 .... but you should double check
Answered by cindy
how did you figure that out and its correct it has the same volume and width
Answered by Reiny
new box would be 12 by 16 by x
12(16)(x) = original volume = 12^3 = 1728
x = 1728/(12(16) ) = 9
Answered by cindy
so they both share an equal material?
Answered by Reiny
no, they have the same volume, but different surface areas (material used)

in original, you would have 6 equal squares
each of 12 by 12 or 144 inches^2
so the surface area of the box including top and bottom = 6(144) or 864 square inches

surface area of the new box
= top and bottom + fron and back + two ends
= 2(16 x 12) + 2(16 x 9) + 2( 12 x 9) = 888 square inches

Make a sketch to see how the calculations developed.
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