We want to construct a closed box with a square base. We only have 20m^2 of material to use in construction of the box. Assuming that all the material is used in the construction process, determine the maximum volume that the box can have to the nearest hundredth of a cubic meter.
dripcima24
Answered question
2022-09-30
We want to construct a closed box with a square base. We only have of material to use in construction of the box. Assuming that all the material is used in the construction process, determine the maximum volume that the box can have to the nearest hundredth of a cubic meter.
Let the dimensions of the base be t while its height is h
Surface area of the box
Its volume
Substituting value of h into the formula for volume and then finding the derivative to find the value of t and h, gives the answer as 6.09 square meters.
Can someone confirm this answer for me
Answer & Explanation
smh3402en
Beginner2022-10-01Added 11 answers
Solving the surface equation for h, plugging the result in the volume equation and computing the local maximum of this function of t does work. The maximal volume comes out to cubic meters as you computed. Did you notice that the optimum is an exact cube?
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