Question

Water is falling on a surface, wetting a circular area that is expanding at a rate of 8mm^2/s How fast is the radius of the wetted area expanding when the radius is 173mm?  (Round your answer to four decimal places.) Options are: 0.0074 mm/s 0.0462 mm/s 135.8738 mm/s 0.0147 mm/s

Answer 1

we know that area of a circular region is given by,

differentiate both the side with respect to t we can say that,

we have to find the rate of change of radius hence we can say that,

As given circular area is expanding at a rate of 8 mm² per second hence we have dA/dt = 8

we have to find the rate of change of radius of circular area when radius is 173 mm hence we have r = 173

we can write,

rounding to 4 decimal places we can say that,

as radius in mm and time in seconds we can say that,

Hence we can say that radius of a wetted area is expanding at a rate of 0.0074 mm/s