Let A be the area of a circle with radius r. If dr/dt=5, find dA/dt when r=3. Round your answer to the nearest tenth.

Question

Let A be the area of a circle with radius r. If dr/dt=5, find dA/dt when r=3. Round your answer to the nearest tenth.

Answer 1

Area of the circle:

A=pi*r^2

Rate of change of the area wrt time:

dA/dt=2*pi*r*dr/dt

=2*pi*3*5

=30 (3.14)

=94.2

Answer 2

A = pi(r^2)

A' = 2pirr'

A' = 2pi(3)(5) = 30pi

= about 30(3.141593) = 94.23779

dA/dt =about 94.2 unit length per unit of time

= instantaneous rate of change of the Area when radius =3 and dr/dt = 5