calculus........

Question

The height of a cylinder is increasing at a rate of 7 inches per​ second, while the radius is decreasing at a rate of 4 inches per second. If the height is currently

57 ​inches, and the radius is 19 ​inches, then find the rate of change in the volume.

ROUND YOUR ANSWER TO ONE DECIMAL

PLACE.​( The formula for the volume of a cylinder is  

V=πr2h.)

The rate of change in the volume is

____

Answer 1

dV/dt = π(2rhdr/dt + r²dh/dt) = π(2·19·57·(- 4) + 19²·7) = - 6137π in³/s = - 19280 in³/s

Answer 2

Given:

dh/dt = 7 in/s

dr/dt = -4 in/s

V=πr²h

Find dV/dt when h = 57 and r = 19

dV/dt = π(r² dh/dt + 2rh dr/dt) Using the product rule.

Just substitute in the values to evaluate dV/dt.

The units will be in³/s.