In the xy-plane, the graph of the equation x^2 + y^2 = r^2 is a circle. If the area of the circle is 49π, what is the value of r?
Correct: A
The area of a circle is given by the formula A = πr^2.
We are given that the area of the circle is 49π.
Set the formula equal to the given area:
πr^2 = 49π
Divide both sides by π:
r^2 = 49
Take the square root of both sides to find r. Since r represents a radius, it must be positive:
r = sqrt(49)
r = 7.