To find the volume of Michelle's cube, we will use the formula for the volume of a cube, which is given by:
\[ V_{cube} = s^3 \]
where \( s \) is the length of one side of the cube. Since Michelle's cube has a height of 6 centimeters, and in a cube, the height is equal to the length of a side, we have:
\[ s = 6 \text{ cm} \]
Now we can calculate the volume of the cube:
\[ V_{cube} = 6^3 = 6 \times 6 \times 6 = 216 \text{ cm}^3 \]
Now, we know that Tasha's pyramid has the same height and base area as Michelle's cube. The height of Tasha's pyramid is also 6 centimeters.
Next, we need to find the base area of the cube. The base of a cube is a square, so its area is given by:
\[ \text{Base Area}_{cube} = s^2 = 6^2 = 36 \text{ cm}^2 \]
Now, let's find the volume of Tasha's pyramid. The formula for the volume of a pyramid is:
\[ V_{pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Substituting in the values we have:
\[ V_{pyramid} = \frac{1}{3} \times 36 \text{ cm}^2 \times 6 \text{ cm} \]
Calculating this gives:
\[ V_{pyramid} = \frac{1}{3} \times 216 \text{ cm}^3 = 72 \text{ cm}^3 \]
Thus, the volumes are:
- Volume of Michelle's cube: \( 216 \text{ cm}^3 \)
- Volume of Tasha's pyramid: \( 72 \text{ cm}^3 \)
Final Answer:
- Volume of Michelle's cube: 216 cm³
- Volume of Tasha's pyramid: 72 cm³