Question

the circumference of the third circle is 20 cm, and point j is the center of the circle. find the approximate length of the radius and the diameter. first find the approximate length of the diameter. remember, you can multiply the diameter by π, or about 3.14, to find the circumference.

Explanation:

Step1: Recall the circumference - diameter formula

The formula for the circumference of a circle is $C=\pi d$, where $C$ is the circumference and $d$ is the diameter. Given $C = 20$ cm and $\pi\approx3.14$, we can solve for $d$.
$d=\frac{C}{\pi}$

Step2: Calculate the diameter

Substitute $C = 20$ cm and $\pi\approx3.14$ into the formula:
$d=\frac{20}{3.14}\approx6.37$ cm

Step3: Recall the radius - diameter relationship

The radius $r$ of a circle is related to the diameter $d$ by the formula $r=\frac{d}{2}$.
$r=\frac{d}{2}$

Step4: Calculate the radius

Substitute $d\approx6.37$ cm into the formula:
$r=\frac{6.37}{2}\approx3.18$ cm

Answer:

Radius: approximately $3.18$ cm, Diameter: approximately $6.37$ cm