A balloon is inflated so its volume V = (4/3)πr³ increases at 8π cm³/s…

Question

A balloon is inflated so its volume V = (4/3)πr³ increases at 8π cm³/s. When r = 2 cm, the rate of change of radius is:

Accepted Answer

B. $1/2$ cm/s (correct via chain rule)

dV/dt = 4πr² × dr/dt. Given dV/dt = 8π, r = 2: 8π = 4π(4) × dr/dt → dr/dt = 8π / 16π = 1/2 cm/s.

Answer

$2$ cm/s (incorrect substitution)

Answer

$1$ cm/s (units misapplied)

Answer

$8\pi$ cm/s (no factor of r²)