Question

Find the exact area of a circle having the given circumference. 3pi

Answer 1

Answer:

A = (9/4)*pi units^2

Step-by-step explanation:

The equation for the circumference of a circle is C = 2*pi*r, where r is the radius.  Given that the actual value of the circumference is 3 pi, we equate this 3 pi to 2*pi*r:  3 pi = 2*pi*r.  

Dividing both sides of this equation by pi, we get 3 = 2r, so that r = 3/2.

The formula for the area of a circle of radius r is A = pi*r^2.

Here r = 3/2, so the area of this circle is

A = pi*(3/2 units)^2 = pi(9/4) units^2, or   A = (9/4)*pi units^2.