Area of sector of a circle bounded by an arc of length 6π cm is equal to 24 π cm2 . Find the radius of the circle
Share
Area of sector of a circle bounded by an arc of length 6π cm is equal to 24 π cm2 . Find the radius of the circle
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
[tex]\underline{\textbf{Given:}}[/tex]
[tex]\mathsf{Area\;of\;a\;sector\;is\;24\,\pi\;cm^2}[/tex]
[tex]\mathsf{and \;its\;arc\;length\is\;6\,\pi\;cm}[/tex]
[tex]\underline{\textbf{To find:}}[/tex]
[tex]\textsf{Radius of the circle}[/tex]
[tex]\underline{\textbf{Solution:}}[/tex]
[tex]\mathsf{Area\;of\;a\;sector\;=\;24\,\pi\;cm^2}[/tex]
[tex]\implies\mathsf{\dfrac{l\,r}{2}=\;24\,\pi}[/tex]
[tex]\implies\mathsf{\dfrac{(6\,\pi)r}{2}=\;24\,\pi}[/tex]
[tex]\implies\mathsf{(3\,\pi)r=\;24\,\pi}[/tex]
[tex]\implies\mathsf{r=\dfrac{24\,\pi}{3\,\pi}}[/tex]
[tex]\implies\boxed{\mathsf{r=8\;cm}}[/tex]
[tex]\therefore\textsf{Radius of the circle is 8 cm}[/tex]