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)

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).