To find the volumes of Michelle's cube and Tasha's pyramid, we need to calculate each volume using the appropriate formulas.
Step 1: Calculate the Volume of Michelle's Cube
The formula for the volume \( V \) of a cube with side length \( s \) is given by:
\[ V = s^3 \]
Since the height of Michelle's cube is 6 centimeters, and all sides of a cube are equal, we have:
\[ s = 6 \text{ cm} \]
Now, we can calculate the volume:
\[ V = 6^3 = 6 \times 6 \times 6 \]
Calculating it step-by-step:
- \( 6 \times 6 = 36 \)
- \( 36 \times 6 = 216 \)
Thus, the volume of Michelle's cube is:
\[ V = 216 \text{ cubic centimeters} \]
Step 2: Find the Base Area of the Cube
The base area \( A \) of Michelle's cube is the area of one face of the cube, which can be calculated as:
\[ A = s^2 = 6^2 = 36 \text{ square centimeters} \]
Step 3: Calculate the Volume of Tasha's Pyramid
The formula for the volume \( V \) of a pyramid with a base area \( A \) and height \( h \) is:
\[ V = \frac{1}{3} A h \]
We know the base area \( A \) of Tasha's pyramid is the same as the base area of Michelle's cube, which is \( 36 \text{ cm}^2 \), and the height \( h \) is \( 6 \text{ cm} \).
Now we can substitute these values into the formula:
\[ V = \frac{1}{3} \times 36 \times 6 \]
Calculating it step-by-step:
- First, calculate \( 36 \times 6 \):
\[ 36 \times 6 = 216 \]
- Then, compute \( \frac{1}{3} \times 216 \):
\[ \frac{1}{3} \times 216 = 72 \]
Therefore, the volume of Tasha's pyramid is:
\[ V = 72 \text{ cubic centimeters} \]
Summary of Results
- Volume of Michelle's cube: \( 216 \text{ cm}^3 \)
- Volume of Tasha's pyramid: \( 72 \text{ cm}^3 \)