The area of a circle increases at a rate of 2 cm 2
/s. a. How fast is the radius changing when the radius is 3 cm ? b. How fast is the radius changing when the circumference is 4 cm ? a. Write an equation relating the area of a circle, A, and the radius of the circle, r. A=π 2
(Type an exact answer, using π as needed.) Differentiate both sides of the equation with respect to t. dt
dA
=(2πr) dt
dr
(Type an exact answer, using π as needed.) When the radius is 3 cm, the radius is changing at a rate of (Type an exact answer, using π as needed.) b. When the circumference is 4 cm, the radius is changing at a rate of (Type an exact answer, using π as needed.)