Question

Take a square sheet of paper of side 10cm. Four small squares are to be cut from the
corners of the square sheet and then the paper folded at the cuts to form an open box.
What should be size of the square cut so that the volume of the open box is maximum?

Answer 1

Answer:

hi friend

Step-by-step explanation:

Take a square sheet of paper of side 10cm. Four small squares are to be cut from the corners of the square sheet and then fold the paper at the cuts to from an open box with maximum volume. What should be the size of squares cut so that the volume of the open box is maximum.

Let say Size of square cut = x * x cm

Then height of Open box = x cm

Length & Breadth of open box = 10 - 2x cm

Volume of box = (10 - 2x)(10 -2x)x cm³

= ( 100 + 4x² - 40x)x

= 100x + 4x³ - 40x²

dV/dx = 100 + 12x² - 80x

dV/dx = 0

12x² - 80x + 100 = 0

=> 3x² - 20x + 25 = 0

=> 3x² - 15x - 5x + 25 = 0

=> 3x(x - 5) -5(x -5) = 0

=> (3x - 5)(x - 5) = 0

=> x = 5/3 x = 5

d²V/dx² = 24x - 80

for x = 5 d²V/dx² = 40 ( +ve) => x = 5 will give minimum volume

for x = 5/3 d²V/dx² = -40 ( -ve) => x = 5/3 will give maximum volume

Size of square cut = (5/3) * (5/3)

hope this helped you

mark it as brainlist.......

Answer 2

Answer:

5/3

Step-by-step explanation:

Let the Size of square cut=xx cm

therefore ,

height of Open box = x cm

and

Length & Breadth of open box = 10 - 2x cm

=> Volume of box = (10-2x)(10-2x}x cm

= ( 100 + 4x - 40x)x

= 100x + 4x 40x

dV/dx = 100 + 12x² - 80x

dV/dx = 0

12 x 80x + 100 = 0

=> 3x - 20x + 25 = 0

=> 3x - 15x - 5x + 25 = 0

=> 3x(x 5) -5(x -5) = 0

=> (3x - 5)(x 5) = 0

=> x = 5/3 or x=5

dV/dx = 24x - 80

for if

x= 5

then,

dV/dx? = 40 ( +ve) => x=5 will give minimum volume

for if

x= 5/3

then ,

dV/dx² = -40 (-ve) => x = 5/3 will give maximum volume

therefore,

Size of square cut = (5/3) (5/3)

hope I am helpful to you