Let V be the volume of the snowball, r be the radius of the snowball, and d be the diameter of the snowball. We know that the volume of a sphere is given by V = (4/3)πr^3, and the radius and diameter are related by d = 2r.
We are given that dV/dt = 2 cm^3/sec, and we want to find dD/dt when r = 2 cm.
Using the chain rule, we can write:
dV/dt = dV/dr * dr/dt
To find dV/dr, we differentiate the volume formula with respect to r:
dV/dr = 4πr^2
Substituting the given values, we get:
2 = (4/3)π(2)^2 * dD/dt
Simplifying the equation, we get:
dD/dt = 3 / (4π) cm/sec
Therefore, when the radius is 2 cm, the diameter of the snowball is increasing at a rate of 3 / (4π) cm/sec.