Question

in the chart below, the circumference, c, of a circle is given. find the values of r (radius), d (diameter), and a (area) for this particular circle. leave π in your answers. (type exact answers, using π as needed.) c = 24π ft

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is $C = 2\pi r=\pi d$. Given $C = 24\pi$ ft. Since $C = 2\pi r$, we can solve for $r$.
$2\pi r=24\pi$. Divide both sides by $2\pi$: $r=\frac{24\pi}{2\pi}=12$ ft.

Step2: Find the diameter

Since $d = 2r$ and $r = 12$ ft, then $d=2\times12 = 24$ ft.

Step3: Calculate the area

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r = 12$ ft into the formula: $A=\pi\times(12)^{2}=144\pi$ ft².

Answer:

$r = 12$ ft, $d = 24$ ft, $A=144\pi$ ft²