Question

An open box A is made from a square piece of tin by cutting equal squares S at the corners and folding up the remaining flaps. Another open box B is made similarly using one of the squares S. If U and V are the volumes of A and B respectively, then which of the following is not possible?

• A. U > V
• B. V > U
• C. U = V
• D. Minimum value of U > Maximum value of V

Answer 1

The correct option is D

Minimum value of U > Maximum value of V

Let the side of tin = a

So, U = $(a-2x{)}^{2}x$

Where x is the side of square which has been cut.

Similarly, V = $(x-2y{)}^{2}y$

Where y is the side of square which has been cut.

Minimum value of U = 0

Minimum value of V = 0

So, U > V and V > U and U = V are possible

But minimum value of U = 0

It cannot be greater than maximum value of V.