Question

g the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing when the diameter is 100 mm?

Answer 1

125,664 mm³/s

Explanation:

V = (4/3)πr³

dV/dt = (4π/3) × 3r² × dr/dt

dV/dt = 4πr² × dr/dt

dr/dt = 4 mm/s

d = 100 mm; r = 50 mm

dV/dt = 4π(50 mm)² × 4 mm/s

dV/dt = 125,664 mm³/s