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  • A spherical balloon in filled with 4500 pi cubic meters of helium gas . if a leak in the balloon causes the gas to escape at the rate of 72 pi cubic meters per minute, then the rate at which the radius of the balloon decreases 49 minutes after the

A spherical balloon in filled with 4500 pi cubic meters of helium gas . if a leak in the balloon causes the gas to escape at the rate of 72 pi cubic meters per minute, then the rate at which the radius of the balloon decreases 49 minutes after the leakage , is.

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Solution:  Total volume of gas =4500pi m^3

                 Volume decreses in 49 min. =72pi imes 49=3528pi

                 Gas left after  49 min.=4500pi-3528pi=972pi

               herefore    Radius after 49 minutes is given by

                                  frac43pi r^3=972piRightarrow r=9

               Now ,         V=frac43pi r^3

            herefore         fracmathrmd Vmathrmd t=4pi r^2fracmathrmd rmathrmd t

            Rightarrow         72pi=4pi imes 81fracmathrmd rmathrmd tRightarrow fracmathrmd rmathrmd t=frac29

Posted by

Deependra Verma

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