Asked by michael garguilo
A box with an open top is to be constructed from a square piece of cardboard, 24 inches wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.
Answers
Answered by
mathhelper
let size of cut-out be x inches by x inches
V = x(24-2x)^2 = 4x^3 - 96x^2 + 576x , where x < 12
dV/dx = 12x^2 - 192x + 576 = 0 for a min of V
x^2 - 16x + 48 = 0
(x-4)(x-12) = 0
x = 4 or x - 12, but x 12 , so x = 4
largest volume = x(24-2x)^2
= 4(16)^2 = 1024 inches^2
V = x(24-2x)^2 = 4x^3 - 96x^2 + 576x , where x < 12
dV/dx = 12x^2 - 192x + 576 = 0 for a min of V
x^2 - 16x + 48 = 0
(x-4)(x-12) = 0
x = 4 or x - 12, but x 12 , so x = 4
largest volume = x(24-2x)^2
= 4(16)^2 = 1024 inches^2
Answered by
michael garguilo
1728 inches
Answered by
mathhelper
Why are you posting "1728 inches"?
What is that supposed to mean?
What is that supposed to mean?
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