Answered

Explore a wide range of topics and get answers from experts on IDNLearn.com. Get step-by-step guidance for all your technical questions from our knowledgeable community members.

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

Sagot :

Skamal2002idn

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.

Learn more about Volume:

https://brainly.com/question/13338592

#SPJ2

Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.