Solve this: Water is poured into inverted conical vessel of which the radius of the base is 2m and height - Maths - Application of Derivatives

Question

Solve this:
Water is poured into inverted conical vessel of which the radius of
the base is 2m and height 4m, at the rate of 77 liter/minute The
rate at which the water level is rising at the instant when the
depth is 70 cm is:(use π = 22/7)
(1) 10 cm/min (2) 20 cm/min (3) 40 cm/min (4) none

Brijendra Pal · Accepted Answer

Here for cone r = 2 m = 200 cmh = 4 m = 400 cm and dVdt= 77 litre/minute = 77000 cm3/minuteV = 13πr2hhere r = h2sp V = πh3×h24=πh312differentiate wrt t dVdt= π12×ddth3= 3πh212dhdt 77000= πh24×dhdtNow wen h is 70 cm then dhdt=77000×4×722×70×70=20 cm/minute

Solve this: Water is poured into inverted conical vessel of which the radius of the base is 2m and height 4m, at the rate of 77 liter/minute. The rate at which the water level is rising at the instant when the depth is 70 cm is:(use π = 22/7). (1) 10 cm/min (2) 20 cm/min (3) 40 cm/min (4) none

Solve this:
Water is poured into inverted conical vessel of which the radius of the base is 2m and height 4m, at the rate of 77 liter/minute. The rate at which the water level is rising at the instant when the depth is 70 cm is:(use $π$ = 22/7).
(1) 10 cm/min (2) 20 cm/min (3) 40 cm/min (4) none