Homework SourseSuppose that the radius r and height h is related to the vol
Suppose that the radius r and height h is related to the volume V of a right cylinder by the equation V = TTr2*h.
a) How is dV/dt related to dr/dt if h is constant?
b) How is dV/dt related to dh/dt if r is constant?
c) How is dV/dt related to dr/dt and dh/dt if neither r nor h is constant?
a) How is dV/dt related to dr/dt if h is constant?
b) How is dV/dt related to dh/dt if r is constant?
c) How is dV/dt related to dr/dt and dh/dt if neither r nor h is constant?
Solution
ln V = Ln ((1/3) pi) + 2 ln r + ln h dV/V = 2 dr/r + dh/h dV = V (2 dr/r + dh/h) How is dV/dt related to dh/dt if r is constant? dV/dt = (V/h) dh/dt How is dV/dt related to dr/dt if h is constant? dV/dt = 2 (V/r) dr/dt How is dV/dt related to dr/dt and dh/dt if neither r nor h is constant? dV/dt = V [ (2/r) dr/dt + (1/h) dh/dt]
