A rectangular piece of cardboard measuring 20 inches by 39 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each
Such square. What is the maximum volume of this box? If necessary, round to 2 decimal places.
A) $1364.09$ in. $^ { 3 }$
B) $29,578.83$ in. 3
C) $1490.83$ in. 3
D) $631.5 \mathrm { in } ^ { 3 }$

Question

A rectangular piece of cardboard measuring 20 inches by 39 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each
Such square. What is the maximum volume of this box? If necessary, round to 2 decimal places. 
A) $1364.09$ in. $^ { 3 }$
B) $29,578.83$ in. 3
C) $1490.83$ in. 3
D) $631.5 \mathrm { in } ^ { 3 }$

Quizplus · Accepted Answer

The volume of the box is given by the function $ V(x) = x(20-2x)(39-2x) $. To find the maximum volume, take the derivative, set it to zero, and solve for $ x $. The maximum volume is approximately $ 1490.83 $ cubic inches.

A Rectangular Piece of Cardboard Measuring 20 Inches by 39 1364.091364.091364.09

A Rectangular Piece of Cardboard Measuring 20 Inches by 39 $1364.09$