Philip P. answered • 06/19/14

Affordable, Experienced, and Patient Geometry Tutor

Width = W

Length = 2W

Height = h

Height = h

Volume = 2300 cm

^{3}= L*W*h = 2W*W*h = 2W^{2}hSo h = 2300/2W

^{2}= 1150/W^{2}Area = 2*(W*h) + 2*(2W*h) + W*2W = 6900/W + 2W

^{2}[Substituted 1150/W^{2}for h, L = 2W]To find the minimum Area, take the derivative of the AREA wrt W, set it to zero, and solve for W:

d(Area)/dW = -6900W

^{-2}+ 4W0 = -6900W

^{-2}+ 4W6900/4 = W

^{3}1725 = W

^{3}**12 ≅ W**[11.993 rounded to 12]

**L = 2W = 24**[23.986 rounded to 24]

**h = 1150/W**[7.995 rounded to 8]

^{2}= 8CHECK:

Volume = 12*24*8 = 2304 [Within rounding error]