Respuesta :
Answer:
The approximate area of the smaller circle is;
[tex]28.26\text{ }in^2[/tex]Explanation:
Given that the radius of a smaller circle is half the length of the radius of a larger circle.
Let R and r represent the radius of the larger and smaller circle respectively;
[tex]R=2r[/tex]The area of the smaller circle will be;
[tex]A_s=\pi r^2[/tex]while the area of the larger circle will be;
[tex]A_l=\pi R^2[/tex]substituting R = 2r;
[tex]\begin{gathered} A_l=\pi R^2 \\ A_l=\pi(2r)^2 \\ A_l=\pi(2^2r^2) \\ A_l=4\pi r^2 \end{gathered}[/tex]We can now replace the area of the smaller circle;
[tex]\begin{gathered} A_l=4\pi r^2 \\ \text{And we know that;} \\ A_s=\pi r^2 \\ so; \\ A_l=4A_s \\ \therefore \\ A_s=\frac{A_l}{4} \end{gathered}[/tex]Given in the question;
The area of the larger circle is 113.04 square inches.
[tex]A_l=113.04\text{ }in^2[/tex]Substituting the area of the larger circle;
[tex]\begin{gathered} A_s=\frac{A_l}{4} \\ A_s=\frac{113.04}{4} \\ A_s=28.26\text{ }in^2 \end{gathered}[/tex]Therefore, the approximate area of the smaller circle is;
[tex]28.26\text{ }in^2[/tex]