Answer:
about 6.52 cm/s
Step-by-step explanation:
The radius of the cone is 3/12 = 1/4 of its height, so the radius of the water surface at the time of interest is (5 cm)/4 = 1.25 cm.
The area of the water's surface is ...
A = πr² = π(5/4 cm)² = 25π/16 cm²
The rate of change of depth multiplied by this area will give the rate of change of volume.
dV/dt = (25π/16 cm²)(dh/dt)
dh/dt = (32 cm³/s)/(25π/16 cm²) = 512/(25π) cm/s ≈ 6.52 cm/s
The water is rising at the rate of about 6.52 cm/s.
