Question

Let A be the area of a circle with radius r. If dr/dt=5, find dA/dt​ when r=3.

A. dA/dt=30π
B. dA/dt=15π
C. dA/dt=45π
D. dA/dt=25π

Answer 1

To find dA/dt when r=3, we differentiate the formula for the area of a circle with respect to time and plug in the given values. The result is dA/dt = 30π.

Step-by-step explanation:

In this question, we are given that dr/dt = 5 and r = 3. We need to find dA/dt. We can use the formula for the area of a circle, which is A = πr². Differentiating both sides of this equation with respect to time, we get dA/dt = 2πr(dr/dt). Plugging in the given values, we have dA/dt = 2π(3)(5) = 30π.