# MATH!!

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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?

• MATH!! -

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

• MATH!! -

how did you figure that out and its correct it has the same volume and width

• MATH!! -

new box would be 12 by 16 by x
12(16)(x) = original volume = 12^3 = 1728
x = 1728/(12(16) ) = 9

• MATH!! -

so they both share an equal material?

• MATH!! -

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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