Question

Please help me

A sheet of cardboard 3 ft by 4 ft will be made in a box by cutting equal sized squares from each corner and folding up the four edges. What will be the dimension of the box with largest volume.

Answer 1

To find the dimensions of the box with the largest volume, you need to determine the size of the squares that will be cut from each corner of the cardboard sheet. The dimension of the box with the largest volume will be 1 ft by 2 ft by 1 ft.

Step-by-step explanation:

To find the dimensions of the box with the largest volume, we need to determine the size of the squares that will be cut from each corner of the cardboard sheet.

Let's say the length of each side of the square is x feet.

The dimensions of the resulting box will then be (3-2x) feet by (4-2x) feet by x feet.

To maximize the volume, we can find the value of x that will maximize the expression (3-2x)(4-2x)(x). We can do this by using calculus or by finding the critical points.

By calculating the derivatives and analyzing the critical points, we can determine that the dimension of the box with the largest volume will be 1 ft by 2 ft by 1 ft.