Question

Area of a Segment

Find the area of the segment of a circle whose radius is 6 inches formed by a central angle of 50°.

Short answer

The area of the segment of a circle is $A=15.71inch{e}^2$

Step-by-step solution

Step 1.  Given information     

The given data from the question is$$\begin{gathered} radius=6inches \\ Centerangle=50 \end{gathered}$$

Step 2.Find the area of the circle

The area of the circle is given by $A={\mathrm{\pi r}}^2$

Now the area of the segment of the given circle having a center angle $50$islocalid="1647241758060" role="math" $$\begin{gathered} A=\frac{\theta }{360}\pi r^2 \\ =\frac{50}{360}\times \frac{22}{7}\times 6^2 \\ =5\times \frac{22}{7} \\ =15.71inc{h}^2 \end{gathered}$$