JanetZappulla
Answered

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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?

Sagot :

konrad509
The center is at the origin and the point [tex](3,0)[/tex] lies on the circle, so [tex]r=3[/tex]

[tex]A=\pi r^2\\ A=\pi \cdot3^2\\ A=9\pi\\ A\approx28.27[/tex]
calculista

we know that

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

[tex] x^{2} +y^{2} =r^{2} [/tex]


step 1

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

substitute the values of

[tex] x=3\\ y=0 [/tex]

in the equation of the circle above

so

[tex] 3^{2} +0^{2} =r^{2} [/tex]

[tex] 3^{2} =r^{2} [/tex]

[tex] r =3 [/tex]


step 2

with the radius find the area of the circle

area of the circle is equal to

[tex] A=\pi *r^{2} [/tex]

for [tex] r=3 [/tex]

[tex] A=\pi *3^{2} [/tex]

[tex] A=28.27 [/tex]units²

therefore


the answer is

the area of the circle to the nearest hundredth is [tex] A=28.27 [/tex]units²

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