14th sum plz

Asked by lovemaan5500 | 20th Aug, 2019, 05:10: PM

Expert Answer:

Let r denotes the radius of the raindrop after t minutes.
radius is decreasing as the rate of change of r must be negative.
Let V be the volume of the raindropand S be its surface area.
begin mathsize 16px style straight V equals 4 over 3 πr cubed space and space straight S equals 4 πr squared end style
begin mathsize 16px style dv over dt straight alpha space straight S
fraction numerator begin display style dv end style over denominator begin display style dt end style end fraction equals negative kS end style
begin mathsize 16px style 4 over 3 straight pi 3 straight r squared dr over dt equals negative straight k 4 πr squared
fraction numerator begin display style dr end style over denominator begin display style dt end style end fraction equals negative straight k end style
Integrating we get
r = -kt + c
At time t = 0 and radius is r0 
r0 = c
r = -kt + r0

Answered by Sneha shidid | 20th Aug, 2019, 06:24: PM