Question

From each corner of a square sheet of side $8cm$, a square of side $\gamma cm$ is cut. The remaining sheet is folded into a cuboid. The minimum possible volume of the cuboid formed is $M$ cubic $cm$. If $y$ is an integer, then find $M$.

• A. 32
• B. 18
• C. 36
• D. 12

Answer 1

Answer: (D)

Length $=$ Breadth $=(8-2\gamma )cm$ and height $=\gamma cm$.
Its volume $=(8-2\gamma )(8-2\gamma )\gamma$
$=(8-2\gamma {)}^{2}y$ cubic $cm$.
$8-2y>0$, i.e., $y<4$ and $y$ is an integer.
$\therefore y=1$ or 2 or 3 .
Among these values of $\gamma$, volume is minimum when $y=3$.
When $y=3$, volume $=12c{m}^3$.
$\therefore M=12$.