The volume v of a right circular cylinder of radius r and heigh h is v = pi r^2 h 1. how is dv/dt related to dr/dt if h is constant and r varies with time? 2. how is dv/dt related to dh/dt if r is constant and h varies with time? 3. how is dv/dt related to dh/dt and dr/dt if both h and r vary with time?

In general, the volume



has total derivative



If the cylinder's height is kept constant, then and we have



which is to say, and are directly proportional by a factor equivalent to the lateral surface area of the cylinder ().

Meanwhile, if the cylinder's radius is kept fixed, then



since . In other words, and are directly proportional by a factor of the surface area of the cylinder's circular face ().

Finally, the general case ( and not constant), you can see from the total derivative that is affected by both and in combination.

A5 miles because when you look at the chart count how many times it goes into it i don’t even know wha,t i’m saying anymore mpbut long stor6 short it’s 5 miles