# 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

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## Question:

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

Rewrite as:

Express as a function

Hence, the required function is: