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aSquares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 17 ft by 10 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way b. Suppose that in part (a) the original piece of cardboard is a square with sides of length sFind the volume of the largest box that can be formed in this way

Respuesta :

The volume of a box is the amount of space in it.

The volume of the largest box is 361.186 [tex]ft^3[/tex]

given

The dimension of the cardboard is given as:

length = 17ft

width = 10ft

Assume the cut-out is x.

So, the dimension of the box is:

length = 17 - 2x ft

width = 10 - 2x ft

height = x ft

The volume of the box is:

volume = [tex](17 - 2x) \times (10 - 2x) \times x[/tex]

volume = [tex]299x + 4x^3 - 72x^2[/tex]

putting the equation up to 0

[tex]299x + 4x^3 - 72x^2 = 0[/tex]

on solving this we get

x = 2.67

now putting the value in this equation we get

[tex]299(2.67) + 4(2.67)^3 - 72(2.67)^2 = v\\v = 361.186[/tex]

Hence, the maximum value of the box is 361.186 [tex]ft^3[/tex]

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