Answer:
a ) dAt/dt = 50,24 in/min
dh/dt = - 0,125 in/min
Step-by-step explanation:
The area of the top is At :
At = π*r²
a) Tacking derivatives with respect to time:
dAt/dt = 2* π*r * dr/dt
At t = t₁ r = 16 in and dr/dt = 0,5
Then
dAt/dt = 2*3,14*16*0,5 in/min
a ) dAt/dt = 50,24 in/min
b) The volume of the cylinder is:
Vc = π*r²*h ( where h is the heigh of the cylinder )
Tacking derivatives with respect to time
dVc/dt = 2* π*r*h*dr/dt + π*r²*dh/dt
But dVc/dt = 0 since the volume remains constant, then:
π*r²*dh/dt = - 2* π*r*h*dr/dt
r*dh/dt = - 2*h*dr/dt
dh/dt = - 2*0,5*2/16 in/min
dh/dt = - 0,125 in/min
-16