"An open gift box is to be made from a square piece of material by cutting 2 centimeter squares from each corner and turning up the sides. The volume of the finished gift box is to be 200 cubic centimeters. Find the size of the original piece of material."

The sides of the box are labeled x.

Is this a closed box, or an open box?

Assuming open box.

dimension of material= ((x+2)*2+x )
d=3x+4

but x^3=200
x=cubrt 200

size oriainal material: 3cubrt200+4 along each side.

It's open. Thanks!

To find the size of the original square piece of material, we need to determine the value of x.

The volume of a rectangular prism (which is what the gift box is) is given by the formula: Volume = Length × Width × Height.

In this case, since the gift box is made from a square piece of material, the length and width of the box will be equal, and we'll use x to represent both of them.

When we cut out 2 centimeter squares from each corner and fold up the sides of the material, the resulting box will have dimensions of (x - 4) cm × (x - 4) cm × 2 cm.

So, the volume of the box can be written as: Volume = (x - 4) × (x - 4) × 2.

We are given that the volume of the box is 200 cubic centimeters. Therefore, we can set up the following equation:
200 = (x - 4) × (x - 4) × 2.

To solve this equation, let's simplify it step by step.

First, let's divide both sides of the equation by 2:
100 = (x - 4) × (x - 4).

Next, let's take the square root of both sides to eliminate the square:
√100 = √((x - 4) × (x - 4)).

Simplifying this further, we have:
10 = x - 4.

Now, let's isolate x by adding 4 to both sides of the equation:
10 + 4 = x.

Therefore, the size of the original square piece of material is 14 centimeters.