Question

A rectangular sheet of 45 cm by 24 cm is to be made into a box without top by cutting of square from

Answer 1

Ask the full question bro

Answer 2

let the side of square be x

Then remaining dimensions of cuboid for volume is

length45−2x, width 24−2x and height x

Volume(v)=(45−2x)(24−2x)x

dx

dv

=(45−2x)(24−2x)−2x(24−2x)−2x(45−2x)

dx

dv

=12(x

2

−23x+90)=12(x−5)(x−18)

Now

dx

dv

=0 at x=5,18

Now,

dx

2

d

2

v

=12(2x−23)

at x=5

dx

2

d

2

v

<0

∴atx=5

that is side of square for which we will get maximum volume