Question

if the area of circle d is 49π square cm, which option will solve for the radius, r?
o r = √(49π/π)
o r = 49π/π
o r = √(49π/2π)
o r = 49π/π

Explanation:

Step1: Recall area formula

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius.

Step2: Substitute given area

Given $A = 49\pi$, we have $49\pi=\pi r^{2}$.

Step3: Solve for $r$

Divide both sides of the equation $49\pi=\pi r^{2}$ by $\pi$: $\frac{49\pi}{\pi}=\frac{\pi r^{2}}{\pi}$, which simplifies to $49 = r^{2}$. Then take the square - root of both sides: $r=\sqrt{49}=7$ (we consider the positive value since radius is non - negative). Starting from $A=\pi r^{2}$, we can solve for $r$ in general as $r = \sqrt{\frac{A}{\pi}}$. Substituting $A = 49\pi$ into $r=\sqrt{\frac{A}{\pi}}$, we get $r=\sqrt{\frac{49\pi}{\pi}}$.

Answer:

$r=\sqrt{\frac{49\pi}{\pi}}$ (corresponding to the correct option among the ones you provided where the intended area value is used in the formula for radius calculation from the area of a circle formula)