A rectangular box is built by cutting out square corners from a

9" by 11" piece of cardboard, then folding the resulting flaps up to form the height. Let x represent the sides of the square corners being cut out. Express the volume of the box as a function of x.
V(x)=_____________________.
What will the volume be if 1" squares are cut out?
With 1 squares cut out, the volume will be __________ cubic inches.

V(x) = x (9 - 2x) (11 - 2x)

plug in 1 for x and solve for V

To find the volume of the box as a function of x, we need to determine the dimensions of the base after the square corners are cut out.

When the x-length squares are cut out from each corner, the resulting base dimensions will be (9-2x) inches by (11-2x) inches. The height of the box will be x inches.

Therefore, the volume of the box can be expressed as V(x) = (9-2x) * (11-2x) * x.

To find the volume when 1-inch squares are cut out (x = 1), we can substitute x = 1 into the function V(x).

V(1) = (9-2(1)) * (11-2(1)) * 1
= (9-2) * (11-2) * 1
= 7 * 9 * 1
= 63 cubic inches.

Therefore, with 1-inch squares cut out, the volume of the box will be 63 cubic inches.

To find the volume of the box as a function of x, we need to determine the dimensions of the box and multiply them together.

The dimensions of the box will be (9 - 2x) by (11 - 2x) by x, where (9 - 2x) represents the length of the base, (11 - 2x) represents the width of the base, and x represents the height.

Therefore, the volume of the box can be expressed as:

V(x) = (9 - 2x)(11 - 2x)(x)

To find the volume when 1" squares are cut out, we substitute x = 1 into the volume function:

V(1) = (9 - 2(1))(11 - 2(1))(1)
= (9 - 2)(11 - 2)(1)
= (7)(9)(1)
= 63 cubic inches

Therefore, with 1" squares cut out, the volume of the box will be 63 cubic inches.