If 40sq. Feet of sheet metal are to be used in construction of an open tank with a square base. Find the dimension of maximum volume
Answers
Given : 40sq. Feet of sheet metal are to be used in construction of an open tank with a square base.
To find : Dimension of box to have maximum volume
Solution:
Let say Side of Square base = x feet
and height = h feet
Surface Area of open tank = x² + 4xh
x² + 4xh = 40 ( Sheet metal available )
=> h = (40 - x²) /4x
Volume V = x²h
= x² (40 - x²) /4x
= x(40 - x²)/4
= 10x - x³/4
dV/dx = 10 - 3x²/4
put dV/dx = 0
=> 10 - 3x²/4
=> x² = 40/3
=> x = 2√(10/3)
d²V/dx² = - 6x/4 < 0
Hence will give maximum volume
h = (40 - x²) /4x = (20/3) / 2√(10/3)
= √(10/3)
Dimensions are
2√(10/3) ft , 2√(10/3) ft , √(10/3) ft
Volume = (40/3)√(10/3) ft³
Learn More:
A sheet of area 40 m2 in used to make an open tank with a square ...
https://brainly.in/question/10126107
A square of x cm is cut from each corner of a square metal sheet of ...
https://brainly.in/question/13516236
A open box with a square base is to be made. Its total surface area is ...
https://brainly.in/question/11774623