Verified Answer :

konrad509

The center is at the origin and the point \((3,0)\) lies on the circle, so \(r=3\)

\(A=\pi r^2\\ A=\pi \cdot3^2\\ A=9\pi\\ A\approx28.27\)

calculista

we know that

the equation of a circle with the center at the origin is equal to

\(x^{2} +y^{2} =r^{2}\)


step 1

with the point (3,0) find the value of the radius

substitute the values of

\(x=3\\ y=0\)

in the equation of the circle above

so

\(3^{2} +0^{2} =r^{2}\)

\(3^{2} =r^{2}\)

\(r =3\)


step 2

with the radius find the area of the circle

area of the circle is equal to

\(A=\pi *r^{2}\)

for \(r=3\)

\(A=\pi *3^{2}\)

\(A=28.27\)units²

therefore


the answer is

the area of the circle to the nearest hundredth is \(A=28.27\)units²

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