Question

write as simple and short as possible. Michelle creates a cube with a height of 6 centimeters. Her friend Tasha creates a square-based pyramid with the same height and base area as Michelle’s cube. Find the volume of Michelle’s cube and use it to find the volume of Tasha’s pyramid. Show all work.(4 points)

Answer 1

To find the volumes, we start with Michelle’s cube.

**Volume of the cube:**

The formula for the volume of a cube is:
\[
V = s^3
\]
where \( s \) is the side length.

Given the height of the cube is 6 cm, the side length \( s \) is also 6 cm.

\[
V = 6^3 = 6 \times 6 \times 6 = 216 \, \text{cm}^3
\]

**Volume of Tasha’s pyramid:**

The formula for the volume of a pyramid is:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

The base of Tasha’s pyramid is a square with the same area as the base area of Michelle’s cube. The area of the base of the cube (which is square) is:
\[
\text{Base Area} = s^2 = 6^2 = 36 \, \text{cm}^2
\]

Now, substituting the base area and height (6 cm) into the pyramid volume formula:
\[
V = \frac{1}{3} \times 36 \times 6
\]
\[
V = \frac{1}{3} \times 216 = 72 \, \text{cm}^3
\]

**Final results:**
- Volume of Michelle's cube: \( 216 \, \text{cm}^3 \)
- Volume of Tasha's pyramid: \( 72 \, \text{cm}^3 \)