Math, asked by sneha4999, 1 year ago

Four small squares of side x are cut out of a square of side 12 cm to make a tray by folding the edges. What is the value of so that the tray has the maximum volume?

Answers

Answered by danielochich
15
When small square of side x is cut at the corners, the dimensions will reduce by 2x


Area of base = (12 – 2x)(12 – 2x)

                      = 144 – 48x + 4x^2


Height of tray = x


Volume = base area x height


          V = (144 – 48x + 4x^2)x


             = 144x – 48x^2 + 4x^3


At maximum volume:

dV/dx = 0


144 – 96x + 12x^2 = 0


12x^2 – 96x + 144 = 0


x^2 – 8x + 12 = 0


x^2 – 6x – 2x + 12 = 0


x(x – 6) -2(x – 6) = 0


(x – 2)(x – 6) = 0


Either x = 2 or x = 6
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