We havea watertank shapedas an invertedright circularcone.Supposethat waterflowsinto the tank at
the rate of At whatrate is the waterlevelrisingwhenthe heightof the waterin the tank is
feet?
Solution:
We first note that this problempresentssomechallengesthat the otherexamplesdid not.
Whenwe differentiatethe originalequation, we get
.The difficultyhere is that we haveno informationaboutthe radiuswhenthe waterlevelis at feet. So we
needto relatethe radiusa quantitythat we do knowsomethingabout.Startingwith the originalequation,
let’s find a relationshipbetween and Let be the radiusof the surfaceof the wateras it flowsout of
the tank.
Notethat the two trianglesare similarand thus correspondingpartsare proportional.In particular,