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Water is dropped at the rate of `2m^(2)//s` into a cone of semivertical angel of `45^(@)`. The rate at which periphery of water surface changes when height of water in the cone is 2 m, isA. `0.5m//s`B. `2m//s`C. `3m//s`D. `1m//s` |
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Answer» Correct Answer - D Given that `(dV)/(dt)=2` `rArr" "(d)/(dt)((1)/(3)pir^(3))=2` `rArr" "pir^(2).(dr)/(dt)=2` `rArr" "(dr)/(dt)=(2)/(pir^(2))` `rArr" "(d)/(dt)(2pir)=(4)/(r^(2))" (i)"` When h = 2 m `rArr" "r=2m` Hence, `(d(2pir))/(dt)=(4)/(4)=1m//s` |
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