Solve the problem
-A rectangular piece of cardboard measuring 15 inches by 45 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 $\mathrm { x }$ 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) $36,689.54$ in $^ { 3 }$
B) $1065.03 \mathrm { in } ^ { 3 }$
C) $3565.03 \mathrm { in } ^ { 3 }$
D) $3052.78$ in $^ { 3 }$

Question

Quizplus · Accepted Answer

The volume of the box is given by $ V = x(15-2x)(45-2x) $. To find the maximum volume, take the derivative of $ V $ with respect to $ x $, set it to zero, and solve for $ x $. The maximum volume is approximately $ 1065.03 $ cubic inches.

Solve the Problem -A Rectangular Piece of Cardboard Measuring 15 x\mathrm { x }x

Solve the Problem
-A Rectangular Piece of Cardboard Measuring 15 $\mathrm { x }$