A box with an open top is to be constructed from a square cardboard, 6 m wide, by cutting out the same small squares from each of the four corners and bending up the sides. Find the largest volume that such a box can have. What is the dimension x (in meters) of the small squares that need to be cut out? Explain, and show all relevant calculations.

Question

Priscilla Mosley

Mathematics

15 March, 06:05

A box with an open top is to be constructed from a square cardboard, 6 m wide, by cutting out the same small squares from each of the four corners and bending up the sides. Find the largest volume that such a box can have. What is the dimension x (in meters) of the small squares that need to be cut out? Explain, and show all relevant calculations.

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Answers (1)

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Aliya Haynes · Answer 1

V = (y) ^2 * (x)

Step-by-step explanation:

3-2x = y or 3-y = 2x

V = (3-2x) ^2 * (x)

V = (4x^2 - 12x + 9) * (x)

V = 4x^3 - 12x^2 + 9x

dV/dx = 12x^2 - 24x + 9

dV/dx = 0 for maximum: 12x^2 - 24x + 9 = 0

Solve for x using the quadratic formula

x = [-b + -sqrt (b^2-4ac) ]/2a

where a = 12, b = - 24, c = 9