Question

move the correct values into the formula to solve for the area of the sector move one answer to each box $a=\frac{1}{2}(\hspace{2cm})^2(\hspace{2cm})$

Explanation:

Step1: Identify the radius and angle

The radius $r = 9$ cm and the central - angle $\theta=20^{\circ}$. First, convert the angle from degrees to radians. We know that to convert degrees to radians, we use the formula $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. So, $\theta = 20\times\frac{\pi}{180}=\frac{\pi}{9}$ radians. The formula for the area of a sector of a circle is $A=\frac{1}{2}r^{2}\theta$ (where $\theta$ is in radians).

Step2: Substitute values into the formula

Substitute $r = 9$ and $\theta=\frac{\pi}{9}$ into the formula $A=\frac{1}{2}r^{2}\theta$. We get $A=\frac{1}{2}(9)^{2}(\frac{\pi}{9})$.

Answer:

The first box should have $9$ and the second box should have $\frac{\pi}{9}$