If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 10 cm.

Answer 1

This is a related rates problem

The surface area of a snowball S = π D² is decreasing with the rate of 2 cm²/min, where D is the diameter of the snowball

dS/dt = d (π D²) / dt = 2π D (dD/dt) = 2 cm²/min

solving for dD/dt = 1/(π D) cm²/min

When D = 10 cm, dD/dt = 1/(10π) cm/min ≈ 0.03 cm/min