how fast is the radius?

Question

the final answer is a decimal The area of a circular slick is growing at the raye of 30 km^2 per day. How fast is the radius increasing when the radius is 5km? Hint: пr^2. Use tha chain rule

Answer 1

A = пr^2

dA/dr = 2пr

You are given the rate of increase of surface area,

i.e. dA/dt = 30 km^2/day

The chain rule lets us write

dA/dt = (dA/dr)*(dr/dt)

i.e. dA/dt = (2пr)*(dr/dt)  using dA/dr = 2пr

so, dA/dt = (10п)*(dr/dt)   when r = 5 km

and 30 = (10п)*(dr/dt)

Finally dr/dt = 3/п = 0.95493 km/day