differentiating relative rates:
oil spilled from a ruptured tanker spreads in a circle whose area increases at a rate of 4 `mi^2` /hr. how fast is the radius of the spill increasing when the area is 25 `mi^2`
Area of a circle `A=pir^2`
Both A and r are functions of t, so differentiate implicitly with respect to t.
It is given that the area of the circle increases at a rate of `4 (mi^2)/(hr).`
`rArr 4= pi*2r(dr)/dt` ...............(i)
We have to find `(dr)/dt` when A=25.
Substituting the value of r in eq(i) we get:
Therefore, when the area is `25 mi^2` the radius of the spill is increasing at a rate of `2/(5sqrtpi)` mi/hr.