What is the volume of the largest box that can be made from a square piece of cardboard with side lengths of 24 inches by cutting equal squares from each corner and turning up the sides?

1024 in³

Step-by-step explanation:

Volume = (24 - 2x)(24 - 2x)(x)

= 576x - 96x² + 4x³

dV/dx = 576 - 192x + 12x² = 0

x² - 16x + 48 = 0

x² - 12x - 4x + 48 = 0

x(x - 12) - 4(x - 12) = 0

(x - 12)(x - 4) = 0

x = 4, x = 12

x can not be 12,

Because 24 - 2(12) = 0

So x = 4

Volume = (24 - 8)(24 - 8)(4)

= 1024

.19875994384

step-by-step explanation:

1699/ 8548

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