An open gift box is to be made from a square piece of material by cutting four-centimeter squares

from the corners and turning up the sides. The volume of the finished box is to be 576 cubic
centimeters.

How to find the size of the original piece of material?

The original square has side of length x. So,

(x-8)(x-8)(4) = 576

what is the answer of this question

To find the size of the original piece of material, we need to follow these steps:

Step 1: Label the size of the square piece of material as 'x'. This represents the length and width of the material in centimeters.

Step 2: Cut four centimeter squares from each corner of the square material. This will reduce both the length and width of the material by 8 centimeters (4 cm from each side).

Step 3: After cutting out the squares, the resulting length and width of the material will be (x - 8) centimeters.

Step 4: Fold up the sides of the material to form a box. The height of the box is 4 centimeters since the squares you cut from the corners are folded up to create the height.

Step 5: Using the formula for the volume of a rectangular prism (Volume = Length * Width * Height), we can calculate the volume of the box:

Volume = (x - 8) * (x - 8) * 4

Step 6: Set the volume equal to 576 cubic centimeters and solve for x:

576 = (x - 8) * (x - 8) * 4

Step 7: Simplify the equation:

576 = 4(x^2 - 16x + 64)

144 = x^2 - 16x + 64

x^2 - 16x - 80 = 0

Step 8: Solve the quadratic equation either by factoring, completing the square, or using the quadratic formula. In this case, we can factorize it:

(x - 20)(x + 4) = 0

Step 9: Set each factor equal to zero and solve for x:

x - 20 = 0 or x + 4 = 0

x = 20 or x = -4

Since the size of the original piece of material cannot be negative, the only reasonable solution is x = 20.

So, the original piece of material is a square with each side measuring 20 centimeters.