Answer: 4/9π
Step-by-step explanation:
Surfacearea of snowball(SA) =4πr^2
dSA/dT = - 10cm^2/min
d = 9, hence, r = 9/2 = 4.5
Taking the derivative of surface area with respect to time:
dSA/dT = 8πrdr/dt
dSA/dT = - 10, r = 4.5
-10 = 8π(4.5)dr/dt
-10 = 36πdr/dt
Make dr/dt subject of the formula
dr/dt = - 10/36π
d = 2r
Differentiating d with respect to time, 't'
dd/dt = 2dr/dt
Therefore, 2dr/dt = 2*(dr/dt)
2×(- 10/36π) = - 20/36π
= -4/9π
Therefore, rate by which diameter decreases when diameter is 9cm is
4/9 π