You are planning to make an open rectangular box from a 25-in.-by-49-in. piece of cardboard by cutting congruent squares from the corners and folding up the sides. What are the dimensions of the box of largest volume you can make this way, and what is its volume?

The dimensions of the box are 38.48 x 14.48 x 5.26 in.

Step-by-step explanation:

We will have a piece of cardboard with squares of side x cut from the corners to make a open box.

The volume of the box can be written as:

To calculate the maximum volume, we derive and equal to zero

We apply the quadratic equation to know the roots of the equation

The first solution is physically impossible, as the side that is cut would be bigger than 25.

So the real solution is for x=5.26 in.

Then, the dimensions of the box are:

the statemwnt is the company makes small and large snow cone cups.

large=it holds more then the small

small=it holds less then the large