Question

To open the next door, your team has to construct a box that can hold themaximum amount of silver pieces. One of your members has a 10x14 piece of cardboard to make the box. You must figure out the max volume that can be attained, as well as the dimensions. Type your answers in the following order:max volume, height, width, length (separate with commas, no spaces, round to one decimal place).

Answer 1

To determine the maximum volume of the box, you need to find the dimensions that will give you the largest volume. Since you have a 10x14 piece of cardboard, you can cut square corners from each side of the cardboard and fold it to create a box. To maximize the volume, take the derivative of the volume equation, set it equal to zero, solve for x, and substitute the value back into the dimensions equation.

Step-by-step explanation:

To determine the maximum volume of the box, you need to find the dimensions that will give you the largest volume. Since you have a 10x14 piece of cardboard, you can cut square corners from each side of the cardboard and fold it to create a box.

The dimensions of the box will be the length and width of the original cardboard minus twice the length of the square corners cut from each side. In this case, the length and width of the box will be 10 - 2x and 14 - 2x, where x is the length of the square corner.

To maximize the volume, you can take the derivative of the volume equation V = lwh, where l = 10 - 2x, w = 14 - 2x, and h = x. Set the derivative equal to zero and solve for x to find the value that maximizes the volume. Substituting this value back into the dimensions equation will give you the dimensions of the box. Use these dimensions to calculate the maximum volume.