Answer:
59.11221 in^3/s
Step-by-step explanation:
Given dr/dt = 0.6 in/s
Find dV/dt when r = 2.8 in.
[tex]V=\frac{4\pi r^3}{3}\\[/tex]
so [tex]\frac{dV}{dr}=4\pi r^2\\[/tex]
[tex]\frac{dV}{dt}=\frac{dV}{dr}\cdot\frac{dr}{dt}=4\pi r^2\cdot\frac{dr}{dt}[/tex]
Use r = 2.8 in and dr/dt = 0.6 in/s
get
[tex]\frac{dV}{dt}=59.11221 in^3/s[/tex]
