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