A rectangular box open at the top is to have a volume of 32c.c. Find the
dimensions of the box that requires the least material for its construction.
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Answer:
48 sq cm
Step-by-step explanation:
Vol = L*W*H = 32 cc
Area = L*W + 2L*H + 2W*H
Assume a square bottom to start, L = W
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Vol = L^2*H = 32 --> H = 32/L^2
Area = L^2 + 4LH --> Area = L^2 + 128/L
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dArea/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
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