Respuesta :
Given:
(a) Circumference of a circle is
[tex]8\pi[/tex]To find: Area of circle
Circumference of circle is given as:
[tex]\text{circumference}=2\pi r=8\pi[/tex]where, r is radius of circle
On solving,
[tex]\begin{gathered} 2\pi r=8\pi \\ r=4 \end{gathered}[/tex]Area of circle is given by formula:
[tex]\begin{gathered} \text{area=}\pi\times r^2^{} \\ =\pi\times4^2 \\ =16\pi \end{gathered}[/tex]Hence, area of circle is :
[tex]=16\pi\text{ squares cm}[/tex](b) Radius of circle is given 'r' and square of length is given 'b'
and they have equal areas.
To find: r in terms of b.
According to the question,
Area of circle= Area of square
[tex]\begin{gathered} \pi\times r^2=b^2 \\ r^2=\frac{b^2}{\pi} \\ r=\sqrt[]{\frac{b^2}{\pi}} \\ =\frac{b}{\sqrt[]{\pi}} \end{gathered}[/tex]Hence,
[tex]r=\frac{b}{\sqrt[]{\pi}}[/tex]