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Question

A rectangular box is to be made from a sheet of 24 inch length and 9 inch width cutting out identical squares of side length x from the four corners and turning up the sides.
What is the value of x for which the volume is maximum?

A
1 inch
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B
1.5 inch
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C
2 inch
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D
2.5 inch
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Solution

The correct option is C 2 inch
Length of the Cuboid = 242x
Breadth of Cuboid =92x
Height of Cuboid =x
Volume of Cuboid V=(242x)(92x)x
V=216x+4x366x2

To know the volume maximum dVdx=0
dVdx=216+12x2132x=0

dVdx=18+x211x=0

(x9)(x2)=0
x=9 or 2
By substituting 9 and 2 we get maximum value of volume for x=2inch

854705_630428_ans_a4fa380f30d148b4b6a8301235da4135.png

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