a packaging company manufactures a cardboard box with a volume of 864 cubic inches. the length of the box is 24 inches, and the ends of the box are square. what is the height of the box in inches?

let the ends be x by x

24x^2 = 864
x^2 = 36
x = 6

To find the height of the box, you can divide the volume of the box by the product of the length and the width. Since the ends of the box are square, the width will be equal to the height.

Let's say the height of the box is "h" inches.

Given:
Volume of the box = 864 cubic inches
Length of the box = 24 inches

We know that the volume of a rectangular prism (like a box) is given by the formula:

Volume = Length * Width * Height

In this case, the length is 24 inches, the height is h inches, and the width is also h inches. So, we can rewrite the formula as:

864 = 24 * h * h

Now we can solve this equation algebraically to find the value of "h."

Divide both sides of the equation by 24 to isolate "h" on one side:

864 / 24 = h * h

36 = h^2

To find the value of "h," take the square root of both sides:

√36 = √(h^2)

6 = h

Therefore, the height of the box is 6 inches.

To find the height of the box, we need to divide the volume of the box by the area of one of the square ends.

The volume of the box is given as 864 cubic inches.
The length of the box is given as 24 inches.

Since the ends of the box are square, we can find the area of one end by squaring the length of the box:

Area of one end = (Length)^2 = (24)^2 = 576 square inches

Now, we can find the height of the box by dividing the volume by the area of one end:

Height = Volume / Area of one end = 864 cubic inches / 576 square inches

Height = 1.5 inches

Therefore, the height of the box is 1.5 inches.