To find the volume of Michelle's cube, we can use the formula for the volume of a cube, which is:
\[ \text{Volume of cube} = \text{side} \times \text{side} \times \text{side} \]
Since the height of the cube is 6 centimeters, all sides are 6 cm.
So,
\[ \text{Volume of cube} = 6 , \text{cm} \times 6 , \text{cm} \times 6 , \text{cm} \]
Calculating that:
\[ 6 \times 6 = 36 \] \[ 36 \times 6 = 216 \]
So, the volume of Michelle's cube is 216 cubic centimeters.
Now, let's find the volume of Tasha's square-based pyramid. The formula for the volume of a pyramid is:
\[ \text{Volume of pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
We know that Tasha's pyramid has the same base area as the base area of Michelle's cube. The base area of the cube is:
\[ \text{Base area of cube} = \text{side} \times \text{side} = 6 , \text{cm} \times 6 , \text{cm} = 36 , \text{cm}^2 \]
Now we can plug this into the volume formula for Tasha's pyramid:
\[ \text{Volume of pyramid} = \frac{1}{3} \times 36 , \text{cm}^2 \times 6 , \text{cm} \]
Calculating that:
\[ 36 \times 6 = 216 \] \[ \text{Volume of pyramid} = \frac{1}{3} \times 216 = 72 \]
So, the volume of Tasha's pyramid is 72 cubic centimeters.
In summary:
- Volume of Michelle's cube: 216 cubic centimeters
- Volume of Tasha's pyramid: 72 cubic centimeters