A spherical ballon is filled with 4500 pie cubic meters of He gas. If a leak in the ballon causes the gas to escape at the rate of 72pie cubic meters per min find the rate at which (min) the radius of the balloon decreases after 49 min?

Question

A spherical ballon is filled with 4500 pie cubic meters of He gas. If a leak in the ballon causes the gas to escape at the rate of 72pie cubic meters per min  find the rate at which (min)  the radius of the balloon decreases after 49 min?

anonymous · Answer

@shubhamsrg  @mukushla  @hartnn

hartnn · Answer

the rate cannot be only in cubic meters....i should be in cubic meters per minute or cubic meters per unit time(like sec,min,hrs)....

shubhamsrg · Answer

exactly !

anonymous · Answer

sorry it isin min

hartnn · Answer

2nd thing,if the rate does not change with time,whatever be the radius,rate remains same......either 72 is the answer or rate should be the function of time....

hartnn · Answer

and as per my guess,rate should decrease with time....

anonymous · Answer

972 pie

anonymous · Answer

@magepker728  we have to find the rate of decreasing radius

shubhamsrg · Answer

well,,
initial volume = 4500
after 49 mins, gas escaped = 72 * 49 = 3528
remaining volume = 4500 - 3528 = 472


final radius,r = [ (472))(3)/(4)(pi) ] ^1/3
given => dV/dt = -72 
V= 4/3 pi r^3
dV/dt = 4/3 pi (3r^2) dr/dt

plug in the values and solve for dr/dt..

anonymous · Answer

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