Differential EquationHard

Question

A spherical balloon is filled with 4500π cubicmeters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters perminute) at which the radius of the balloon decreases 49 minutes after the leakage began is :

Options

A.9/2
B.9/7
C.7/9
D.2/9

Solution


Initially r = 4500 π, r = r0 
r0 = 15m
Now ......(i)
= - 18 t + C
At time t = 49 min      r = 9 m
from eq. (i)
= - 2/9
(Negative sign shows decrement in radii)

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