Volume of Sphere V = (4/3)πr³
Given dV/dt = 2 in³/minute, r = 1/2 = 0.5 inch
dV/dt = dV/dr * dr/dt
V = (4/3)πr³
dV/dr = 3*(4/3)πr³ ⁻ ¹ = 4πr² = 4π*0.5² = 4π*0.25 = π in²
dV/dt = dV/dr * dr/dt
2 in³/minute = π * (dr/dt)
π in² * (dr/dt) = 2 in³/minute
(dr/dt) = (2 in³/minute) / (π in²)
(dr/dt) = (2/π) in/minute.
The radius of the snowball is reducing at (2/π) inches/minute.
