Question

no additional details were added for this assignment. explain how to get the formula for the circumference of a circle. use the drop - down arrows to complete the sentences. π is defined as. we first rewrite the equation using properties of equality to show the formula for the circumference of a circle is. we know the relationship between the lengths of a diameter and a radius of a circle is. so we can also write the formula for the circumference of a circle as

Explanation:

Step1: Recall definition of pi

$\pi$ is defined as the ratio of the circumference $C$ of a circle to its diameter $d$, i.e., $\pi=\frac{C}{d}$.

Step2: Solve for circumference

Using the property of equality, we multiply both sides of the equation $\pi = \frac{C}{d}$ by $d$. So, $C=\pi d$.

Step3: Substitute diameter - radius relationship

We know that $d = 2r$ (where $r$ is the radius of the circle). Substituting $d=2r$ into $C=\pi d$, we get $C = 2\pi r$.

Answer:

$\pi$ is defined as the ratio of the circumference of a circle to its diameter. The formula for the circumference of a circle is $C=\pi d$. The relationship between the length of a diameter and a radius of a circle is $d = 2r$. So we can also write the formula for the circumference of a circle as $C=2\pi r$.