Answer:
-2π square inches per second
Step-by-step explanation:
The lateral surface area is the product of the height and circumference, so can be described by the formula ...
LA = 2πrh
Differentiating with respect to time, we get ...
LA' = 2π(r'h +rh')
Filling in the given values, gives ...
LA' = 2π((-0.5 in/s)(14 in) + (4 in)(1.5 in/s)) = 2π(-7 in²/s +6 in²/s)
= -2π in²/s ≈ -6.283 in²/s . . . . rate of change of lateral area
