Question

EXPLAIN WITH STEPS

The area of a circle is decreasing at a rate of 5 square inches per minute. How fast is the

radius shrinking when the radius is 2 inches in length

Answer 1

Explanation:

Area of a circle is:

A = πr²

Take derivative with respect to time:

dA/dt = 2πr dr/dt

Plug in values and solve:

-5 = 2π (2) dr/dt

dr/dt = -5/(4π)

dr/dt ≈ -0.398

The radius is shrinking at approximately 0.398 in/min.