The area of a circle is changing at a rate of 6 in²/sec At what rate is its radius changing when the radius is 5 in? A) in/sec B) in/sec C) in/sec D) in/sec E) in/sec

Question

Quizplus · Accepted Answer

We know that the formula for the area of a circle is A = πr^2, where r is the radius.

Differentiating both sides with respect to time, we get:

dA/dt = d/dt (πr^2)

dA/dt = 2πr (dr/dt)

We are given that dA/dt = 6 in^2/sec when r = 5 in.

Plugging in these values, we get:

6 in^2/sec = 2π(5 in)(dr/dt)

Solving for dr/dt, we get:

dr/dt = 6/(10π)

dr/dt = 0.19099...

Rounding to two decimal places, we get:

dr/dt ≈ 0.19 in/sec

Therefore, the answer is D) 11ea984b_b1e5_5f87_9029_af34973d0965_TB4005_11 in/sec.

The Area of a Circle Is Changing at a Rate