A rectangular box open at the top is to have a volume of 32 cubic feet. Find its dimensions if the total surface area is minimum

Question

Question

A rectangular box open at the top is to have a volume of 32 cubic feet. Find its dimensions if the total surface area is minimum

LaGrange’s Method Problems

  1. Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2
  2. Discuss maximum or minimum for x^3+y^3-3xy
  3. Find the maxima and minima values of the function f (x, y) =3x+4y on the circle x^2+y^2=1 using method of Lagrange’s multipliers
  4. Find the maximum and minimum values of x^2+y^2 subject to the condition 2x^2+3xy+2y^2=1
  5. If x, y, z are the angles of a triangle, find the maximum value of sin x sin y sin z
  6. A rectangular box open at the top is to have a volume of 32 cubic feet. Find its dimensions if the total surface area is minimum
  7. Show that the rectangular box of maximum value and a given surface area is a cube
  8. Find the volume of the largest rectangular parallelepiped that can be inscribed in the ellipsoid x^2/a^2 +y^2/b^2 +z^2/c^2 =1
  9. Find the dimensions of the rectangular box open at the top of maximum capacity whose surface is 432 sq.cm

 

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