Question

solve the problem.

1. the area of a circle is found by the equation a = πr². if the area a of a certain circle is 81π square centimeters, find its radius r.

a) {9 cm, -9 cm}
b) 9√π cm
c) 9 cm
d) 9π cm

Explanation:

Step1: Substitute given area into formula

Given $A = 81\pi$ and $A=\pi r^{2}$, we substitute to get $81\pi=\pi r^{2}$.

Step2: Solve for $r^{2}$

Divide both sides of the equation $81\pi=\pi r^{2}$ by $\pi$. We have $\frac{81\pi}{\pi}=\frac{\pi r^{2}}{\pi}$, which simplifies to $r^{2}=81$.

Step3: Find the value of $r$

Take the square - root of both sides. Since $r$ represents the radius of a circle (a non - negative quantity), $r=\sqrt{81}=9$ cm.

Answer:

C. 9 cm