This answer key provides the solutions for the Volume of Prisms and Cylinders flip and foldable activity, detailing the formulas and calculations for each shape.

The image you provided is a worksheet that explains how to calculate the volumes of prisms and cylinders using their respective formulas. Below, I will break down each section of the worksheet and explain the solutions step by step.

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1. Volume of a Rectangular Prism

#### Given:
- Base area (\( B \)) = 6 cm²
- Height (\( h \)) = 8 cm

#### Formula:
\[ V = B \cdot h \]

#### Solution:
\[ V = 6 \, \text{cm}^2 \cdot 8 \, \text{cm} = 48 \, \text{cm}^3 \]

#### Answer:
\[ V = 48 \, \text{cm}^3 \]

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2. Volume of a Cube

#### Given:
- Side length = 2 in

#### Formula:
For a cube, the base is a square, so:
\[ B = \text{side}^2 \]
\[ V = B \cdot h \]
Since all sides are equal in a cube, \( h = \text{side} \).

#### Step-by-Step:
1. Calculate the base area (\( B \)):
\[ B = 2 \, \text{in} \cdot 2 \, \text{in} = 4 \, \text{in}^2 \]

2. Calculate the volume (\( V \)):
\[ V = B \cdot h = 4 \, \text{in}^2 \cdot 2 \, \text{in} = 8 \, \text{in}^3 \]

#### Answer:
\[ V = 8 \, \text{in}^3 \]

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3. Volume of a Triangular Prism

#### Given:
- Base of the triangle (\( b \)) = 5 units
- Height of the triangle (\( h_{\text{triangle}} \)) = 2 units
- Height of the prism (\( h_{\text{prism}} \)) = 6 units

#### Formula:
The base area (\( B \)) of the triangular prism is the area of the triangular base:
\[ B = \frac{1}{2} \cdot b \cdot h_{\text{triangle}} \]
Then, the volume (\( V \)) is:
\[ V = B \cdot h_{\text{prism}} \]

#### Step-by-Step:
1. Calculate the base area (\( B \)) of the triangle:
\[ B = \frac{1}{2} \cdot 5 \, \text{units} \cdot 2 \, \text{units} = 5 \, \text{units}^2 \]

2. Calculate the volume (\( V \)):
\[ V = B \cdot h_{\text{prism}} = 5 \, \text{units}^2 \cdot 6 \, \text{units} = 30 \, \text{cubic units} \]

#### Answer:
\[ V = 30 \, \text{cubic units} \]

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4. Volume of a Cylinder

#### Given:
- Radius (\( r \)) = 3 ft
- Height (\( h \)) = 9 ft

#### Formula:
The base area (\( B \)) of the cylinder is the area of the circular base:
\[ B = \pi r^2 \]
Then, the volume (\( V \)) is:
\[ V = B \cdot h = \pi r^2 \cdot h \]

#### Step-by-Step:
1. Calculate the base area (\( B \)):
\[ B = \pi \cdot (3 \, \text{ft})^2 = \pi \cdot 9 \, \text{ft}^2 = 9\pi \, \text{ft}^2 \]

2. Calculate the volume (\( V \)):
\[ V = B \cdot h = 9\pi \, \text{ft}^2 \cdot 9 \, \text{ft} = 81\pi \, \text{ft}^3 \]

3. Approximate the value using \( \pi \approx 3.14 \):
\[ V \approx 81 \cdot 3.14 = 254.34 \, \text{ft}^3 \]

#### Answer:
\[ V = 81\pi \, \text{ft}^3 \quad \text{(exact)} \]
\[ V \approx 254.34 \, \text{ft}^3 \quad \text{(approximate)} \]

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Summary of Solutions:

1. Rectangular Prism: \( V = 48 \, \text{cm}^3 \)
2. Cube: \( V = 8 \, \text{in}^3 \)
3. Triangular Prism: \( V = 30 \, \text{cubic units} \)
4. Cylinder: \( V = 81\pi \, \text{ft}^3 \) or \( V \approx 254.34 \, \text{ft}^3 \)

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Final Answer:

\[
\boxed{48 \, \text{cm}^3, 8 \, \text{in}^3, 30 \, \text{cubic units}, 81\pi \, \text{ft}^3}
\]