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

115 c.c.

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120 c.c.

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125 c.c.

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130 c.c.

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Solution

The correct option is D
130 c.c.

Volume of box $V = (12 - 2 x)^{2} x$

$V = (144 + 4 x^{2} - 48 x) x$

$V = 4 x^{3} - 48 x^{2} + 144 x$

For maximum volume, $\frac{d v}{d x} = 0$

$\frac{d (4 x^{3} - 48 x^{2} + 144 x)}{d x} = 0 12 x^{2} - 96 x + 144 = 0 x^{2} - 8 x + 12 = 0 \Rightarrow x = 2 o r 6 x \neq 6 s o x = 2 f o r x = 2 V = (12 - 2 \times 2)^{2} \times 2 V_{m a x} = 128 S o V = 130 c . c$

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

The correct option is D 130 c.c. Volume of box V=(12−2x)2x V=(144+4x2−48x)x V=4x3−48x2+144x For maximum volume, dvdx=0 d(4x3−48x2+144x)dx=012x2−96x+144=0x2−8x+12=0⇒x=2 or 6x≠6so x=2for x=2V=(12−2×2)2×2Vmax=128So V=130 c.c