Answer:
Step-by-step explanation:
The volume of a cone is ⅓πR²h
With an included angle of 60°, tan30 = R/h
R = htan30 = h(1 / √3) = h/√3
so the volume of this cone in terms of h is
V = ⅓π(h/√3)²h = ⅟₉πh³
V = ⅟₉πh³
the differential of the volume will equal the derivative of the function relative to height times the differential of the height
dV = ⅓πh²•dh
dividing each side by a differentially small period of time
dV/dt = ⅓πh²•dh/dt
dh/dt = (3/πh²)dV/dt
At the point in question the volume is 3000π cm³ so h is
3000π = ⅟₉πh³
h = 30 cm
and we're told dV/dt = 5 cm³/s
dh/dt = (3/π(30)²)5
dh/dt = 15/900π = 1/60π or approximately 0.0053 cm/s
