Edith wants to make a paperweight at pottery class. She wants the paperweight to have a pyramid-like shape with a base area of 120 square centimeters, and she wants it to weigh 400 grams. The density of the clay she is using is 1.6 grams per cubic centimeter.

What should be the height of the paperweight?
centimeters

Step 1 ：Edith wants to make a paperweight at pottery class. She wants the paperweight to have a pyramid-like shape with a base area of 120 square centimeters, and she wants it to weigh 400 grams. The density of the clay she is using is 1.6 grams per cubic centimeter.

Step 2 ：We need to find the height of the paperweight. The volume of a pyramid is given by the formula \(V = \frac{1}{3} \times \text{base area} \times \text{height}\). We know the base area and we know the weight of the paperweight, which is equal to the volume times the density of the clay.

Step 3 ：We can set up the equation \(400 = 1.6 \times (\frac{1}{3} \times 120 \times \text{height})\) and solve for height.

Step 4 ：Solving the equation gives us the height of the paperweight.

Step 5 ：Final Answer: The height of the paperweight should be \(\boxed{6.25}\) centimeters.