Calculus - Related Rates
When a metal rod is cooled, its length decreases at a rate of 0.03cm/min and its radius increases at a rate of 0.004cm/min. Find the rate of change of the volume when the length is 1.7m and the radius is 3cm.

I need step by step help please

11.97cm³/min

work is shown below, answer is 11.97 /min as said in your question

Explanation:

V of a metal rod = V of cylinder =

V =

V' = 2rh * r' + (use product rule of differentiation)

plugging in known values now

V' = 2(3 cm)(170 cm) (0.004 cm/min) + (-0.03cm/min)

V' = 2(2.04 /min) - 0.27/min

V' = 12.81769 /min - 0.84823 /min

V' = 11.97 /min