A box is made with square base and open top. The area of the material used is 192 sq. cms. If the volume of the box is maximum, the dimensions of the box are

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4,4,8

2, 2,4

2, 2, 2

8, 8, 4

answer is C.

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Detailed Solution

Verify the formula $x^{2} + 4 x y$

$A r e a o f b o x 192 = a^{2} + 4 ha$
$volume of box = a^{2} h$

$\begin{aligned} = a^{2} \frac{(192 - a^{2})}{4 a} \\ = a (192 - a^{2}) \\ \frac{d v}{d a} = (192 - a^{2}) - 2 a^{2} \\ a^{2} = 64 \\ a = 8, h = 4 \end{aligned}$

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