Question

the area of a circle increases at a rate of 3cm^2/s
a) how fast is the radius changing when the radius is 6cm?
b) how fast is the radius changing when the circumfrence is 5cm?

Answer 1

Answer:

a) 1/(4π) ≈ 0.0796 cm/s

b) 3/5 = 0.6 cm/s

Step-by-step explanation:

Area of a circle is:

A = πr²

Take derivative with respect to time:

dA/dt = 2πr dr/dt

a) When r = 6 cm:

3 = 2π (6) dr/dt

dr/dt = 1/(4π)

dr/dt ≈ 0.0796 cm/s

b) When 2πr = 5 cm:

3 = 5 dr/dt

dr/dt = 3/5

dr/dt = 0.6 cm/s