The equation shown in your image is:

$C = 2\pi r$

This formula represents the circumference (C) of a circle, where $r$ is the radius of the circle, and $\pi$ (pi) is a mathematical constant approximately equal to 3.14159. This equation expresses how the circumference is proportional to the radius.

Explanation:

1. 2π is a constant factor because π is a universal ratio between a circle’s circumference and diameter, and multiplying it by 2 gives the relation with the radius (since diameter = 2 × radius).
2. The larger the radius $r$, the greater the circumference $C$.
3. It’s useful in geometry problems where you need to calculate the perimeter or edge length of a circle.

Would you like me to show a detailed calculation for an example or further derive the formula?

Here are five questions related to this concept:

1. What is the circumference of a circle with a radius of 5 units?
2. How does the circumference change if the radius doubles?
3. Can this formula be rearranged to solve for the radius $r$ in terms of the circumference $C$?
4. How does the circumference relate to the area of a circle?
5. What happens to the circumference if $\pi$ is approximated as 3 instead of 3.14?

Tip: Always remember that circumference relates to linear distance around the edge of the circle, while area refers to the space inside the circle!