Answer:
Rate of change of the diameter is equal to 0.053cm/min
Step-by-step explanation:
A snowball is of the shape of a sphere
Surface area of Sphere (S)= [tex]4*pi*R^2[/tex]
Rate of change of surface area
dS/dt = -4[tex]cm^2/min[/tex]
the negative sign indicates the surface area is decreasing.
Radius = d/2 where d represents diameter
using this is the surface area equation
S = [tex]4*pi*(d/2)^2[/tex]
= [tex]pi*d^2[/tex]
dS/dt = 2*pi*d*d(d)/dt
4 = 2*pi*d*(d)/dt
d(d)/dt = 2/12*pi= [tex]\frac{1}{6pi}[/tex] cm/min
so the rate of change of the diameter is equal to 0.053cm/min
