An inverted cone has a depth of 40 cm and a base radius of 5cm. Water is poured into it at a rate of 1.5 cubic centimetres /minute . find the rate at which the level of water in cone is rising when the depth is 4cm.

explain in great detail

Asked by haroonrashidgkp | 8th Sep, 2018, 04:14: PM

Expert Answer:

begin mathsize 16px style Volume space of space the space cone space equals 1 third πr squared straight h
By space similarity space of space triangles
5 over 40 equals straight r over straight h
straight r equals straight h over 8
Volume equals 1 third straight pi open parentheses straight h over 8 close parentheses squared straight h equals πh cubed over 192
According space to space the space question
dv over dt equals 1.5
fraction numerator straight d πh cubed over 192 over denominator dt end fraction equals 1.5
πh squared over 64 dh over dt equals 1.5
dh over dt equals 96 over πh squared
straight h equals 4 space cm
dh over dt equals 6 over straight pi space cm divided by straight s end style

Answered by Sneha shidid | 9th Sep, 2018, 06:22: PM