coffee is draining from a conical filter of height n diameter 15cm into a cylinderical coffee pot of diameter 15 - Maths - Application of Derivatives

Question

coffee is draining from a conical filter of height n diameter
15cm into a cylinderical coffee pot of diameter 15 cm the rate at
which coffee drains from the filter into the pot is 100 cm/min the
rate in cm/min at which the level in the pot is rising at the
instant when the coffee in the pot is 10cm, is?

Anuradha Sharma · Accepted Answer

The rate at which the level in the pot is increasing can be found out as, So V=πr2h=π×1522×hSo dVdt=π×2254×dhdtHere it is given that dVdt=100cm3/min100=14π×225×dhdtSo dhdt=400225π=169πcm/min