Question

120° 6 cm use the keypad to enter your answer in the box. express it in terms of π (use the π symbol in your answers) a = □ cm²

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $r$ is the radius of the circle.

Step2: Identify values of $\theta$ and $r$

Given that $\theta = 120^{\circ}$ and $r = 6$ cm.

Step3: Substitute values into formula

$A=\frac{120^{\circ}}{360^{\circ}}\times\pi\times(6)^{2}$.
First, simplify $\frac{120^{\circ}}{360^{\circ}}=\frac{1}{3}$, and $(6)^{2}=36$. Then $A=\frac{1}{3}\times\pi\times36$.

Step4: Calculate the area

$A = 12\pi$ $cm^{2}$.

Answer:

$12\pi$