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

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`

Answer 2

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