the area of the sector in terms of r is [tex]10r^2[/tex]
Given :
From the given diagram , the radius of the circle is 5r and length of arc AB is 4r
Lets find out the central angle using length of arc formula
length of arc =[tex]\frac{central-angle}{360} \cdot 2\pi r[/tex]
r=5r and length = 4r
[tex]4r=\frac{central-angle}{360} \cdot 2\pi (5r)\\4r \cdot 360=central-angle \cdot 2\pi (5r)\\\\\\\frac{4r \cdot 360}{10\pi r} =angle\\angle =\frac{4\cdot 36}{\pi } \\angle =\frac{144}{\pi }[/tex]
Now we replace this angle in area of sector formula
Area of sector =[tex]\frac{angle}{360} \cdot \pi r^2\\[/tex]
[tex]Area =\frac{angle}{360} \cdot \pi r^2\\\\Area =\frac{\frac{144}{\pi } }{360} \cdot \pi\cdot 25r^2\\\\Area =\frac{ 144 }{360\pi } \cdot \pi\cdot 25r^2\\\\Area =\frac{ 2 }{5 } \cdot 25r^2\\\\\\Area=10r^2[/tex]
So, the area of the sector in terms of r is [tex]10r^2[/tex]
Learn more : brainly.com/question/23580175
