Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. the cardboard is 10 cm by 10 cm. the volume v(x) in cubic cm of the open top box is a function of the side length x in cm of the square cutouts

The volume of a shape is the amount of space in it;

The volume as a function of side length (x) is:

From the question, we have the dimension of the cardboard to be;

When side length (x) is removed from the cardboard, the dimension of the box becomes:

So, the volume of the box is:

Substitute known values

Expand

Expand

Rewrite as:

Express as a function

Hence, the required function is:

Read more about volume functions at:

link

The domain for x is all real numbers greater than zero and less than 5 com

Step-by-step explanation:

The question is

What is the volume of the open top box as a function of the side length x in cm of the square cutouts?

see the attached figure to better understand the problem

Let

x -----> the side length in cm of the square cutouts

we know that

The volume of the open top box is

we have

substitute

Find the domain for x

we know that

so

The domain is the interval (0,5)

The domain is all real numbers greater than zero and less than 5 cm

therefore

The volume of the open top box as a function of the side length x in cm of the square cutouts is

568

Step-by-step explanation: