Question

The point (3,0) lies on a circle with the center at the origin. What is the area of the circle to the nearest hundredth?

Answer 1

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

Answer 2

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

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