To find the volume of Michelle's cube, we can use the formula for the volume of a cube, which is \( V = s^3 \), where \( s \) is the length of one side. Since the height of the cube is given as 6 centimeters, the side length is also 6 centimeters. Therefore, the volume of the cube is \( 6^3 = 216 \) cubic centimeters.
Next, Tasha creates a square-based pyramid that has the same height and base area as the cube. The base area of the cube can be calculated as \( s^2 \), which is \( 6^2 = 36 \) square centimeters. The volume of the pyramid is given by the formula \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). Substituting the base area and height into this formula, we find that the volume of Tasha's pyramid is \( V = \frac{1}{3} \times 36 \times 6 = 72 \) cubic centimeters. Thus, the volume of Tasha's pyramid is 72 cubic centimeters.