Volume and surface area of sphere : V = (4/3)πr³
S = 4πr²
Rate of volume and surface area :
dV/dt = (4/3)π × 3r² × dr/dt
dS/dt = 4π × 2r × dr/dt
dV/dt = 8 cm³/s ⇒ (4/3)π × 3r² × dr/dt = 8 ⇒ dr/dt = 8 × 1/(4π × 12²) = 0.00441
Now dS/dt = 4π × 2r × dr/dt = 4 × 2π × 12 × 0.00441 = 1.33 cm²/s