Posted by cindy on .
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!! :(

MATH!! 
victoria,
length would be 16 , width 12, and hight 9 .... but you should double check

MATH!! 
cindy,
how did you figure that out and its correct it has the same volume and width

MATH!! 
Reiny,
new box would be 12 by 16 by x
12(16)(x) = original volume = 12^3 = 1728
x = 1728/(12(16) ) = 9 
MATH!! 
cindy,
so they both share an equal material?

MATH!! 
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.