Related rates: shampoo filling a bottle with varying diameter

[fletchea]

A child loves to watch as you fill a transparent plastic bottle with shampoo. Every horizontal cross section of the bottle is circular, but the diameters of the circles have different values. You pour the brightly colored shampoo into the bottle at a constant rate of 17.0 cm3/s.

At what rate is its level in the bottle rising at a point where the diameter of the bottle is = 6.80 cm?

At what rate is its level in the bottle rising at a point where the diameter of the bottle is = 1.39 cm?

no height was given for the problem. I would show attempts at solving but I am pretty lost on the whole thing. any help would be appreciated.

 

[tiny-tim]

welcome to pf!

hi fletchea! welcome to pf!

forget the varying diameter, just answer the question as if the bottle was an ordinary cylinder with diameter 6.80 cm

 

[HallsofIvy]

tiny-tim's answer is for the first question, of course. For the second question treat as a cylinder of diameter 1.39 cm.

 

[tiny-tim]

tiny-tim's answer is for the first question, of course. For the second question treat as a cylinder of diameter 1.39 cm.

awww … you're making it too easy!