Question

A rectangular box, open at the top,is to have given capacity. Find the dimensions of the box least material for its construction.​

Answer 1

L = B = ∛(2V) , H = V/(∛(2V))²   V is the capacity of Box

Step-by-step explanation:

Let say Dimension of Box = L , B & H

Given Capacity  = V

For Minimum surface Area L = B = x

V = LBH

=> H = V/x²

Surface Area = 2 (L + B)H  + LB

S = 2(x + x)(V/x²)  + x²

S = 4V/x + x²

dS/dx  = -4V/x² + 2x

-4V/x² + 2x = 0

=> x³ = 2V

=> x = ∛(2V)

L = B = ∛(2V)

H = V/(∛(2V))²

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Answer 2

Answer:

V is the capacity of the box.