Asked by Kate
determine the dimensions of a rectangular solid (with a square base) with maximum volume if it's surface area is 289 meters
Answers
Answered by
MathMate
With a given symmetric surface area, the maximum volume is achieved with a symmetric shape. In this case, the rectangular solid would become a cube, such that:
6x²=289
x=sqrt(289/6)
volume = x^3 = (289/6)^(3/2)=334.3
and the side = x = 6.94 metres
Using calculus:
If the side of the base is x,
Height, h = (289-2x²)/4x
Volume,
V = x²h
=x²((289-2x²)/(4x))
=289x/4 - x³/2
Calculate dV/dx and equate to zero.
dV/dx = 289/x - 3x²/2 = 0
Solve for x.
6x²=289
x=sqrt(289/6)
volume = x^3 = (289/6)^(3/2)=334.3
and the side = x = 6.94 metres
Using calculus:
If the side of the base is x,
Height, h = (289-2x²)/4x
Volume,
V = x²h
=x²((289-2x²)/(4x))
=289x/4 - x³/2
Calculate dV/dx and equate to zero.
dV/dx = 289/x - 3x²/2 = 0
Solve for x.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.