Question

If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.

Answer 1

Dr/dt = -7 / (pi*r*8)
 
         =  -7 / pi*5*8
       
          = - 0.56 cm/min

Hope this helps

Answer 2

Surface area: S
radius: r
diameter: e
time: t

[dS/dt] = [dS/de]*[de/dt] => de/dt = [dS/dt] / [dS/de]

S = 4pi*r^2 = 4p*i(e/2)^2 = pi*e^2 => dS/de =2pi*e

dS/dt = 7cm^2 / min

de / dt = [2pi*e] / [7cm^2/min] =[7cm^2/min] /  [2pi*10cm]  = 0.11 cm/min