The rapidly increase of radius of spill is
when the area is 8 is 0.9 miles/hr.
let the radius and area of oil spill be r and A .
we have given that,
Area increases at a constant rate of 6 miles²/hr i.e., dA/dt = 9
we have to find out the rapid change in radius of circle i.e., dr/dt = ?
Area of circle (A) = π r²
Takeing the derivative with respect to time
dA/dt = 2 π r × (dr/dt)
Substitute values and solve for dr/dt:
When A = 8 -> 8 = π r²-> r = sqrt(8/π)
putting all values in equation (1) we get,
9= 2 π sqrt(18/π) × (dr/dt)
dr/dt = 9/2(π× sqrt(8/π)) miles/hr
=> dr/dt = 9/10.023 = 0.89
Hence , 0.9miles / hr is rate of change of radius of oil spill when area is 8.
To learn more about Rate of change of radius , refer:
https://brainly.com/question/19672359
#SPJ4
