https://file.aiquickdraw.com/mathbot/file/17276852045385jfq4ksv.jpg

Let's match the descriptions with the correct formulas from the image.

### Descriptions:
1. Volume of a cylinder
2. Volume of a sphere
3. Surface area of a rectangular prism
4. Surface area of a cylinder
5. Surface area of a sphere
6. Circumference of a circle
7. Volume of a hexagonal prism

### Formulas:
- a. \( V = \frac{4}{3} \pi r^3 \)
- b. \( S.A = P h + 2 (\text{area of base}) \)
- c. \( S.A = 4 \pi r^2 \)
- d. \( V = B h \)
- e. \( C = 2 \pi r \)
- f. \( V = \pi r^2 h \)
- g. \( S.A = 2 \pi r h + 2(\pi r^2) \)

### Matching the descriptions with the formulas:

1. **Volume of a cylinder**:  
   Formula: \( f. V = \pi r^2 h \)
   
2. **Volume of a sphere**:  
   Formula: \( a. V = \frac{4}{3} \pi r^3 \)

3. **Surface area of a rectangular prism**:  
   Formula: \( b. S.A = P h + 2 (\text{area of base}) \)

4. **Surface area of a cylinder**:  
   Formula: \( g. S.A = 2 \pi r h + 2(\pi r^2) \)

5. **Surface area of a sphere**:  
   Formula: \( c. S.A = 4 \pi r^2 \)

6. **Circumference of a circle**:  
   Formula: \( e. C = 2 \pi r \)

7. **Volume of a hexagonal prism**:  
   Formula: \( d. V = B h \) (where \( B \) is the area of the hexagonal base)

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Would you like further clarification or details on any of these? Here are five related questions:

1. How do you derive the volume formula for a cylinder?
2. What is the significance of \( 4 \pi r^2 \) in the surface area of a sphere?
3. Why does the surface area formula of a cylinder have two terms related to the radius?
4. How can you calculate the area of the base for a hexagonal prism?
5. How does the circumference formula relate to the radius of a circle?

**Tip:** Always make sure to distinguish between area and volume formulas by looking at the dimensions involved (e.g., square units for area, cubic units for volume).

Match the descriptions with the formulas provided in the image, which include volume and surface area formulas for various geometric shapes.

Learn how to match descriptions of volumes and surface areas of common geometric shapes like spheres, cylinders, prisms, and circles to the correct mathematical formulas. This problem helps with geometry concepts and is suitable for high school students in Grades 9-12.

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