Question

the area of a circle is 36π feet². which of the following represents the circumference, in feet, of the same circle? reference sheet a = πr² c = 2πr a = lw a = 1/2bh c² = a² + b² v = lwh v = πr²h v = 4/3πr³ v = 1/3πr²h v = 1/3lwh the number of degrees of arc in a circle is 360. the number of radians of arc in a circle is 2π. the sum of the measures in degrees of the angles of a triangle is 180. 6 6π 12 12π

Explanation:

Step1: Find the radius from the area formula

Given $A = \pi r^{2}$ and $A = 36\pi$. So, $\pi r^{2}=36\pi$. Divide both sides by $\pi$: $r^{2}=36$, then $r = 6$ (we take the positive value since radius is non - negative).

Step2: Calculate the circumference

Use the formula $C = 2\pi r$. Substitute $r = 6$ into the formula: $C=2\pi\times6 = 12\pi$.

Answer:

D. $12\pi$