To find the volumes of Michelle's cube and Tasha's square-based pyramid, we’ll start with Michelle’s cube.
Step 1: Find the volume of Michelle's cube.
The formula for the volume of a cube is: \[ V = s^3 \] where \(s\) is the length of each side of the cube.
Since Michelle's cube has a height of 6 centimeters, each side of the cube is also 6 centimeters.
Now, we calculate the volume: \[ V = 6 , \text{cm} \times 6 , \text{cm} \times 6 , \text{cm} = 6^3 = 216 , \text{cm}^3 \]
So, the volume of Michelle's cube is 216 cubic centimeters.
Step 2: Find the volume of Tasha's pyramid.
The formula for the volume of a square-based pyramid is: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
We know that Tasha's pyramid has the same base area and height as Michelle’s cube.
Finding the base area: Since the cube has a height of 6 cm, each face of the cube is a square with an area of: \[ \text{Base Area} = s \times s = 6 , \text{cm} \times 6 , \text{cm} = 36 , \text{cm}^2 \]
Using the height of the pyramid: Tasha's pyramid also has a height of 6 cm.
Now we can find the volume of Tasha's pyramid: \[ V = \frac{1}{3} \times 36 , \text{cm}^2 \times 6 , \text{cm} \]
Calculating this step-by-step:
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First, multiply the base area by the height: \[ 36 , \text{cm}^2 \times 6 , \text{cm} = 216 , \text{cm}^3 \]
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Now take one-third of that: \[ V = \frac{216 , \text{cm}^3}{3} = 72 , \text{cm}^3 \]
So, the volume of Tasha's pyramid is 72 cubic centimeters.
Summary:
- Volume of Michelle's cube: 216 cm³
- Volume of Tasha's pyramid: 72 cm³