Question

An open box is made from a sqaure lamina of side $12$cm, by cutting equal squares at the corners and folding up the remaining flaps. The volume of this box cannot be.

• A. $115$c.c.
• B. $120$c.c.
• C. $125$c.c.
• D. $130$c.c.

Answer 1

The correct option is D $130$c.c.

Volume of the box V$=(12-2x{)}^{2}x=(144+4x^2-48x)x=4x^3+144x-48x^2$

For maximum volume $\frac{dv}{dx}=0$

$\frac{d(4x^3+144x-48x^2)}{dx}=0$

$⟹3\times 4x^2+144-2\times 48x=0$

$⟹12x^2+144-96x=0$

$⟹x^2-8x+12=0$

$⟹(x-6)(x-2)=0$

$⟹x=6$ or $x=2$

For $x=6$ Volume V$=(12-12{)}^{2}6=0$

$\therefore x\ne 6$

So, for $x=2$

V$=(12-4{)}^2\times 2=128$

$\therefore$ V${}_{max}=128$ c.c.

Hence, the volume can't be $130$ c.c.