Question

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.​

Answer 1

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

----

Vol = L^2*H = 32 --> H = 32/L^2

Area = L^2 + 4LH --> Area = L^2 + 128/L

----

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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