related rates

Question

(a) if A is the area of the circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt.

its our first day of doing related rates so I'm kinda lost but i got. dA/dt=πr^2 but I'm not sure what to do with the in terms of dr/dt part.

 

(b) suppose oil spills from a ruptured tanker and spreads in a circular pattern. if the radius of the oil spill increases at a constant rate of 1m/s, how fast is the area of the spill increasing when the radius is 30m.

I'm not sure where to start here. do i just plug stuff in ?

 

Answer 1

(a)

 

Use the chain rue.

 

A(r) = πr²

 

dA/dt = π(2r dr/dt) = 2πrdr/dt

 

(b)

 

Use dA/dt from part (a).

 

dA/dt = 2πrdr/dt = 2π(30 m )(1 m/s) = 60π m²/s