Can someone help me with application of differentiation ?

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

d

step-by-step explanation: