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an open rectangular box with square ends is fitted with an overlapping lid that covers the top and front face determine the maximum volume of the box if 1square meter of metal is used in its construction



Answer :

skamal2002

so would it be 8 meters because it has 8 sides 

Volume is a three-dimensional scalar quantity. The maximum volume of the box is 0.8m³.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Surface area of the box = 2x² + 3xy

Surface area of lid = 2xy

Total area = 2x² + 5xy = 6

y = (6-2x²)/5x

Volume of the box, V = x²y

V = x²[(6-2x²)/5x] = (6x/5)-(2x³/5)

Now, for the volume to be the maximum,

dV/dx = 0

(6/5)-(6x²/5) = 0

x² = 1

x = ±1

y = 4/5

Thus, the maximum volume of the box = x²y = (1)²×(4/5) = 0.8 m³

Hence, the maximum volume of the box is 0.8m³.

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