A box without lid having maximum volume is made out of square metal sheet of edge 60 cms by cutting equal square pieces from thefour corners and turning up the projecting pieces to make the sides of the box. The height of the box is

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Solution

The correct option is B 10
Volume of box $= (60 - 2 b)^{2} b$
$\frac{d v}{d b} = 4 (60 - 2 b) b + (60 - 2 b)^{2}$
$= (60 - 2 b) (60 - 6 b)$
$b = 30, 10$
$\frac{d^{2} v}{d b^{2}} > 0$ when $b = 0$
So V is max when $b = 10$

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A box without lid having maximum volume is made out of square metal sheet of edge 60 cms by cutting equal square pieces from thefour corners and turning up the projecting pieces to make the sides of the box. The height of the box is

The correct option is B 10Volume of box=(60−2b)2bdvdb=4(60−2b)b+(60−2b)2=(60−2b)(60−6b)b=30,10d2vdb2>0 when b=0So V is max when b=10

The correct option is B 10
Volume of box $= (60 - 2 b)^{2} b$
$\frac{d v}{d b} = 4 (60 - 2 b) b + (60 - 2 b)^{2}$
$= (60 - 2 b) (60 - 6 b)$
$b = 30, 10$
$\frac{d^{2} v}{d b^{2}} > 0$ when $b = 0$
So V is max when $b = 10$