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The worksheet presents a variety of geometric shapes, and the task is to determine their volumes. Here are the corresponding formulas for each shape type, and I'll walk you through the process of solving them.

### Square Base:
1. **Prism** (Cube):
   - **Formula for volume**: \( V = \text{Base Area} \times \text{Height} \)
   - In the cube, the base area is \( 4 \, \text{cm} \times 4 \, \text{cm} = 16 \, \text{cm}^2 \), and the height is 4 cm.
   - \( V = 16 \, \text{cm}^2 \times 4 \, \text{cm} = 64 \, \text{cm}^3 \)

2. **Pyramid**:
   - **Formula for volume**: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
   - The base area is \( 4 \, \text{cm} \times 4 \, \text{cm} = 16 \, \text{cm}^2 \), and the height is 4 cm.
   - \( V = \frac{1}{3} \times 16 \, \text{cm}^2 \times 4 \, \text{cm} = \frac{1}{3} \times 64 \, \text{cm}^3 = 21.33 \, \text{cm}^3 \)

### Triangle Base:
1. **Prism**:
   - **Formula for volume**: \( V = \text{Base Area} \times \text{Height} \)
   - The given base area is 10 cm², and the height is 9 cm.
   - \( V = 10 \, \text{cm}^2 \times 9 \, \text{cm} = 90 \, \text{cm}^3 \)

2. **Pyramid**:
   - **Formula for volume**: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
   - The given base area is 10 cm², and the height is 9 cm.
   - \( V = \frac{1}{3} \times 10 \, \text{cm}^2 \times 9 \, \text{cm} = 30 \, \text{cm}^3 \)

### Circle Base:
1. **Cylinder**:
   - **Formula for volume**: \( V = \pi r^2 h \)
   - The radius \( r = 5 \, \text{cm} \), and the height \( h = 14 \, \text{cm} \).
   - \( V = \pi \times (5 \, \text{cm})^2 \times 14 \, \text{cm} = \pi \times 25 \, \text{cm}^2 \times 14 \, \text{cm} = 350 \pi \, \text{cm}^3 \approx 1099.56 \, \text{cm}^3 \)

2. **Cone**:
   - **Formula for volume**: \( V = \frac{1}{3} \pi r^2 h \)
   - The radius \( r = 5 \, \text{cm} \), and the height \( h = 7 \, \text{cm} \).
   - \( V = \frac{1}{3} \pi \times (5 \, \text{cm})^2 \times 7 \, \text{cm} = \frac{1}{3} \pi \times 25 \, \text{cm}^2 \times 7 \, \text{cm} = \frac{175 \pi}{3} \, \text{cm}^3 \approx 183.26 \, \text{cm}^3 \)

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Would you like further clarification or more details on any of these steps? Here are five follow-up questions you might consider:

1. How does the relationship between a prism and pyramid affect their volume formulas?
2. What is the significance of the factor \( \frac{1}{3} \) in pyramid and cone volume formulas?
3. How would the volume of the cube change if only the height was doubled?
4. How is the area of the base calculated for shapes like the cone and pyramid if only radius or base length is given?
5. What real-life objects resemble the shapes of prisms, pyramids, and cylinders?

**Tip**: Always ensure you have consistent units when calculating the volume, especially when working with different dimensional shapes!

Determine the volume of the following shapes using the appropriate formula for the given prism and pyramid with square, triangular, and circular bases.

Learn how to calculate the volume of prisms, pyramids, cylinders, and cones using formulas for square, triangular, and circular bases. This problem is suitable for students in Grades 7-9 and covers key geometric formulas and relationships.

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