Water is dripping out from a conical funnel at the uniform rate of 4 cm3/sec. When the slant height of water is 3 cm, find the rate of the decrease of slant height of the water, give that vertical angle of the funnel is 120o.
α=120∘2=60∘
∵rh=tanα
⇒r=tan60∘×h
⇒r=h√3
∴l=√r2+(h)2
⇒l=√3h2+h2
⇒l=2h⇒h=l2
⇒dldt=2dhdt
∵v=13⋅πr2h
⇒v=13π(3h2)h
⇒v=πh3
⇒dvdt=3πh2.dhdt
4=3π(l2)2.dhdt
⇒dhdt=4×43π(3)2=1627π
⇒dldt=2dhdt=3227π cm./sec