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.