Question

a circle has an area of 400 m^2. find the radius. round to the nearest tenth

Answer 1

The area \( A \) of a circle is given by the formula:

\[
A = \pi r^2
\]

where \( r \) is the radius. Given that the area is \( 400 \, \text{m}^2 \), we can set up the equation:

\[
400 = \pi r^2
\]

To solve for \( r \), first divide both sides by \( \pi \):

\[
r^2 = \frac{400}{\pi}
\]

Now, take the square root of both sides to find \( r \):

\[
r = \sqrt{\frac{400}{\pi}}
\]

Calculating \( \frac{400}{\pi} \):

\[
\frac{400}{\pi} \approx \frac{400}{3.14159} \approx 127.32395
\]

Now take the square root:

\[
r \approx \sqrt{127.32395} \approx 11.29
\]

Rounding to the nearest tenth, we get:

\[
r \approx 11.3 \, \text{m}
\]

So, the radius of the circle is approximately \( 11.3 \, \text{m} \).