Final answer:
To find the rate of change of the radius when the area of a circle is increasing at a constant rate, we can differentiate the formula for the area of a circle with respect to time and solve for the rate of change of the radius.
Step-by-step explanation:
To find the rate of change of the radius, we can differentiate the formula for the area of a circle with respect to time. The area of a circle is given by A = πr², where r is the radius. Differentiating this equation with respect to time, we get dA/dt = 2πr(dr/dt).
Given that dA/dt = 88 square meters per second and at the instant when the area is 100π square meters, we can substitute these values into the equation and solve for dr/dt.
Substituting, we have 88 = 2π(r)(dr/dt), and when A = 100π, r = 10.
Plugging in the values, we get 88 = 2π(10)(dr/dt), which simplifies to dr/dt = 88/(20π).
Rounding to three decimal places, the rate of change of the radius is approximately 0.698 meters per second.