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Answer:
Hence the maximum possible volume will be the 778.53 c.c
Step-by-step explanation:
Given:
A rectangle with 13 x 26 dimensions
And corners are cut to form side squares.
To Find:
Maximum possible volume for box
Solution :
Consider a rectangle of 13 x 26 dimension with and side of square at corner be x.
(Refer the attachment)
Now,
Formulating the volume equation for the box
So corner square sides we are going to fold up which makes height of the box
and remaining part will be length and breadth
As shown in fig,
Length=26-x
breadth=13-x
And height will be x
To get maximum volume differentiate the above equation,
Now ,Solve the Quadratic Equation to get x values,
=0
x=[-b±(b^2-4ac)^1/2]/2a
x=[78±Sqrt[(78)^2-4*338*3)]/2*3
x=[78±Sqrt(3028)]/6
x=[78±55.027]/6
x=78+55.027/6 or x=78-55.027/6
x=22.17 or x=3.8288
Use these values in 6x-78 to know which value posses the max and min value for the function.
So when x=22.17
6x-78=6*22.17-78
=55.02>0 i.e function will have minimum value .
When x=3.8288
6*3.8288-78
=-55.0272<0 i.e. Function will have maximum value
Now, the function will defines the maximum volume
