Answer:
Dh/dt = 0,141 ft/min
Step-by-step explanation:
Volume of a cone is:
V(c) = 1/3 *π*r²*h (1)
r is radius of the base, and h is the height.
As the diameter ( 2*r) is three times h
2r = 3h ⇒ r = (3/2)*h
We have DV(t)/dt = 1 ft³
And from equation (1)
V(c) = 1/3 *π*r²*h ⇒ V(t) = 1/3 *π* (3/2*h)² * h
V(t) = 1/3 *π*9/4 *h³ ⇒ V(t) = 3/4*π*h³
Taking derivatives on both sides of the equation
DV(t)/dt = 3/4*π* ( 3 h² Dh/dt)
By substitution we get
1 = 9/4*π*h²* Dh/dt solving for Dh/dt when h = 1 ft
1 = 9/4 *π*(1)²*Dh/dt
Dh/dt = ( 4/9)/π
Dh/dt = 0,141 ft/min
