Answer:
work is shown below, answer is 11.97 [tex]cm^3[/tex]/min as said in your question
Explanation:
V of a metal rod = V of cylinder = [tex]\pi r^{2} h[/tex]
V = [tex]\pi r^{2} h[/tex]
V' = 2[tex]\pi[/tex]rh * r' + [tex]\pi r^{2} h'[/tex] (use product rule of differentiation)
plugging in known values now
V' = 2[tex]\pi[/tex](3 cm)(170 cm) (0.004 cm/min) + [tex]\pi[/tex][tex](3 cm)^2[/tex](-0.03cm/min)
V' = 2[tex]\pi[/tex](2.04 [tex]cm^3[/tex]/min) - 0.27[tex]\pi[/tex] [tex]cm^3[/tex]/min
V' = 12.81769 [tex]cm^3[/tex]/min - 0.84823 [tex]cm^3[/tex]/min
V' = 11.97 [tex]cm^3[/tex]/min
