Q. 125.0( 3 Votes )

Answer :

Side length of big square is 18 cm

Let the side length of each small square be a.

If by cutting a square from each corner and folding up the flaps we will get a cuboidal box with

Length, L = 18 – 2a

Breadth, B = 18 – 2a and

Height, H = a

Assuming,

Volume of box, V = LBH = a(18 - 2a)^{2}

Condition for maxima and minima is

(18 - 2a)^{2} + (a)(- 2)(2)(18 - 2a) = 0

(18 - 2a)[(18 - 2a) - 4a] = 0

(18 - 2a)[18 – 6a] = 0

a = 3, 9

( - 2)(18 – 6a) + ( - 6)(18 – 2a)

For a = 3, = - 72,

For a = 9, = 72,

So for A to maximum

Hence, a = 3 will give maximum volume.

And maximum volume, V = a(18 - 2a)^{2} = 432 cm^{3}

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