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