Answer:
a) The volume of the largest box that can be formed is .
b) The maximum volume of the box:
Explanation:
a) Length of the card board = l = 37 ft
Width of the card board= b = 20ft
Squares with sides of length x are cut out of each corner of a rectangular cardboard to form a box.
Now, length of the box = L = 37 -2x
Breadth of the box ,B= 20- 2x
Height of the box ,H= x
Volume of the box ,V= L × B × H
Putting ,
x = 4.1537 , 14.846
When , x = 4.1537 , (maxima)
The volume of the largest box that can be formed:
The volume of the largest box that can be formed is .
b) Original piece of cardboard is a square with sides of length s.
Length of the card board = l = s
Squares with sides of length x are cut out of each corner of a rectangular cardboard to form a box.
Now, length of the box = L = s -2x
Height of the box ,H = x
Volume of the box ,V= L × L × H
When , (maxima)
The maximum volume of the box: