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Standard XII

Mathematics

Global Maxima

A box is made...

Question

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

4,4,8

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2, 2,4

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8, 8, 4

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2, 2, 2

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Solution

The correct option is B 8, 8, 4
area of box
$192 = a^{2} + 4 h a$
volume of box $= a^{2} h$
$= a^{2} \frac{(192 - a^{2})}{4 a}$
$= a (192 - a^{2})$
$\frac{d v}{d a} = (192 - a^{2}) - 2 a^{2}$
$a^{2} = 64$
$a = 8$ $h = 4$

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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

The correct option is B 8, 8, 4area of box192=a2+4havolume of box =a2h=a2(192−a2)4a=a(192−a2)dvda=(192−a2)−2a2a2=64a=8 h=4

The correct option is B 8, 8, 4
area of box
$192 = a^{2} + 4 h a$
volume of box $= a^{2} h$
$= a^{2} \frac{(192 - a^{2})}{4 a}$
$= a (192 - a^{2})$
$\frac{d v}{d a} = (192 - a^{2}) - 2 a^{2}$
$a^{2} = 64$
$a = 8$ $h = 4$