Question

The circle has center O. Its radius is 6cm, and the central angle a measures 130°. What is the area of the shaded region? Give the exact answer in terms of pi, and be sure to include the correct unit in your answer

Answer 1

13π square centimeters.

Step-by-step explanation:

• The radius of the circle centre O = 6cm

,

• The central angle, α = 130°

The shaded region is a sector.

`\begin{gathered} \text{Area of a sector}=(\alpha)/(360)*\pi r^2 \\ \alpha=\text{Central Angle} \end{gathered}`

Therefore, the area of the shaded region is:

`\begin{gathered} \text{Area of shaded region}=(130)/(360)*\pi*6^2 \\ =(4680\pi)/(360) \\ =13\pi cm^2 \end{gathered}`

The area of the shaded region is 13π square centimeters.