A balloon which always remains spherical, isbeing inflated by pumping in 900 cubic centimetres of gas per second. Findthe rate at which the radius of the balloon is increasing when the radius is15 cm.

A balloon which always remains spherical, isbeing inflated by pumping

1.	A balloon which always remains spherical, isbeing inflated by pumping in 900 cubic centimetres of gas per second. Findthe rate at which the radius of the balloon is increasing when the radius is15 cm.
Answer» Correct Answer - `(dr)/(dt) = 0.32 cm//s` `V =(4)/(3) pi r^(3) rArr (dV)/(dt) = 4pi r^(2).(dr)/(dt) rArr (dr)/(dt) = (900)/(4pir^(2)) = (225)/(pir^(2))` `rArr [(dr)/(dt)]_(r = 15) = (225)/(pi xx (15)^(2)) = (1)/(pi) cm//s`

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A balloon which always remains spherical, isbeing inflated by pumping in 900 cubic centimetres of gas per second. Findthe rate at which the radius of the balloon is increasing when the radius is15 cm.

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