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Home » A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.
A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.
Applications of Derivatives | CBSE | Class 12 | Exercise 6.5 | Maths | NCERT
A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

Each side of square piece of tin is 18 cm.

Let  cm be the side of each of the four squares cut off from each corner.

Then dimensions of the open box formed by folding the flaps after cutting off squares are  and  cm.

Let  denotes the volume of the open box.

  

  

  

= 

    and 

Now  = 0

 

 

  or 

 is rejected because at  length =  which is impossible.

   is the turning point.

At ,  

·  is minimum at  therefore, side of each square to be cut off from each corner for maximum volume is 3 cm.

i

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