What is the least amount of material required to construct a square base box one of whose base is open and whose volume is 2700cm^3?
1 Answer
The least amount of material required to construct a square base box is
Explanation:
Let the side of the square base be
Area of the square base is
If the height of the box is
Area of the lateral side is
Total lateral surface of the box is
Including the base, material consumed will be
Volume of the box is
Given:
Volume of the box is
Equating the volumes
Solving for y
Substituting in the expression for area
Simplifying
Minimizing,
By the principle of maxima and minima
Equating to zero
For
Multiplying throughout by
Simplifying
Substituting the value of x in the expression for Area