7.1 Open Boxes

Front

What is the formula for the volume of an open-top box created from a rectangular sheet of paper after cutting out squares from each corner?

Back

V(x) = (length - 2x)(width - 2x)x, where x is the side length of the cutout.

Front

If a square of side x inches is cut from each corner of a 10 in x 18 in piece of cardboard, what is the volume function V(x)?

Back

V(x) = x(18 - 2x)(10 - 2x).

Front

What is the interval of values for x when making an open-top box from a 12 cm x 16 cm sheet of paper?

Back

0 < x < 6.

Front

What is the appropriate domain for the function V(x) representing the volume of an open-top box when x can take values between -1 and 5?

Back

0 < x < 2.5.

Front

What is the domain of the problem situation when cutting squares from a 10 in x 18 in piece of cardboard?

Back

(0, 5).

Front

How do you determine the maximum value of x when creating an open-top box from a rectangular sheet?

Back

x must be less than half the length of the shorter side of the rectangle.

Front

What does the variable x represent in the context of creating an open-top box from a rectangular sheet?

Back

x represents the side length of the square cutouts from each corner.

Tags

CCSS.8.EE.C.7B

Front

Why is it important to establish a domain for the variable x in volume functions?

Back

The domain ensures that the values of x are physically meaningful and do not result in negative dimensions.

Front

What is the significance of the expression V(x) = (12 - 2x)(16 - 2x)x?

Back

It represents the volume of an open-top box formed from a 12 cm x 16 cm sheet of paper after cutting out squares of side x.

Front

What happens to the volume of the box as the value of x increases?

Back

The volume initially increases, reaches a maximum, and then decreases as x approaches the limits of the domain.