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 be $a$

$⟹U=(a-2x{)}^{2}x$, where $x$ is the side of a square which have been cut.

Similarly, $V=(a-2y{)}^{2}y$, where $y$ is the side of a square which have been cut.

Minimum value of $U=0$

Minimum value of $V=0$

$⟹U>V$, or $V>U$ or $U=V$

But minimum value of $U=0$. So, it can't be greater than maximum value of $V$.

Hence, minimum value of $U>$ Maximum value of $V$ is not possible.