Question

The radius of a right circular cylinder is decreasing at a rate of 5 inches per minute while the height is increasing at a rate of 5 inches per minute. determine the rate of change of the volume when r = 4 and h = 3.

Answer 1

DR/dt= -5inM-¹
dH/dt = 5inM-¹

recall V=πr²h
dV/dr = 2πrh
dV/dh= πr²

dV/dt = ½{ (dH/dt • dV/dH) + (dV/dr • dr/dt)}
dV/dt = ½{ ( 5×πr²) + (2πrh×-5)}
dV/dt = ½{ 5πr² -10πrh}
= ½{ 80π - 120π}
= -20π inM-¹