A rectangular box open at the top is to have a volume of 32 cc find the dimensions of the box that requires least materials to construct it
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▶Vol = L*W*H = 32 cc
▶Area = L*W + 2L*H + 2W*H
▶Assume a square bottom to start, L = W
▶Vol = L^2*H = 32 --> H = 32/L^2
▶Area = L^2 + 4LH --> Area = L^2 + 128/L
▶Area/dL = 2L - 128/L^2 = 0
▶L^3 - 64 = 0
▶L = 4
A box 4 by 4 by 2
▶Area = 16 + 16 + 16
= 48 sq cm
thank you . ..
▶Vol = L*W*H = 32 cc
▶Area = L*W + 2L*H + 2W*H
▶Assume a square bottom to start, L = W
▶Vol = L^2*H = 32 --> H = 32/L^2
▶Area = L^2 + 4LH --> Area = L^2 + 128/L
▶Area/dL = 2L - 128/L^2 = 0
▶L^3 - 64 = 0
▶L = 4
A box 4 by 4 by 2
▶Area = 16 + 16 + 16
= 48 sq cm
thank you . ..
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0
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