The area of a circle is 3\pi \ cm^2. If the radius of this circle is tripled, what is the new area?

(A) 9\pi \ cm^2

(B) 18\pi \ cm^2

(C) 27\pi \ cm^2

(D) 81\pi \ cm^2

Thanks

kadence

10-25-2013, 07:46 PM

The area of a circle with radius r is given by the following formula

A=\pi r^2

So, A=\pi r^2=3\pi \Rightarrow r^2=3 (1)

If the radius of this circle is tripled i.e. 3r the new area is equal to \pi (3r)^2=9\pi r^2 (2)

From (1) and (2) we have that the new area is

A_{new}=9\pi (3)=27\pi \ cm^2

Therefore the correct answer is (C).

Hope these help!!

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