Question

The mechanics at Lincoln Automotive are reboring a 6-in deep cylinder to fit a new piston. The machine they are using increases the cylinders radius one-thousandth of an inch every 4min. How rapidly is the cylinder volume increasing when the bore (diameter) is 3.800in ...?

Answer 1

dr/dt = 0.00025/min
V = πr^2h
dV/dt = 2πrh dr/dt
Here, r = 3.8/2 = 1.9, h = 6
dV/dt = 2π(1.9)(6)(0.00025) = 0.00285π = 0.00895 in^2/min