oil spilled from a tank,spread in a circle whose area increases at a constant rate of 5m/s.How fast is the radius of the spill increasing when the area is 10m^2?

Solution:

Radius: r

Area: pi*r^2

S = pi*r^2

dS/dt = pi* 2r * dr/dt

5 = 2*pi*r*dr/dt

When S = 10, r = 1.785

So

dr/dt = 5/(2*pi*1.785) = 0.446 m/s

So the result is 0.446 m/s