Answer:
[tex]\huge\boxed{A=784\pi\ cm^2\approx2464\ cm^2}[/tex]
Step-by-step explanation:
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
r - radius
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have C = 176cm. Substitute to the formula and calculate the radius r:
[tex]2\pi r=176\qquad|\text{divide both sides by}\ 2\pi\\\\r=\dfrac{176}{2\pi}\\\\r=\dfrac{88}{\pi}\qquad|\text{use}\ \pi\approx\dfrac{22}{7}\\\\r=\dfrac{88}{\frac{22}{7}}\\\\r=88\cdot\dfrac{7}{22}\\\\r=4\cdot7\\\\\boxed{r=28(cm)}[/tex]
Calculate the area:
[tex]A=\pi\cdot28^2=784\pi\approx784\cdot\dfrac{22}{7}=112\cdot22=2464(cm^2)[/tex]
According to the moderator, I should take [tex]\pi\approx3.14[/tex]. You can do it like that. In my opinion, my solution is correct.
