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The radius of an air bubble is increasing at the rate of `1/2c m//s`. At what rate is the volume of the bubble increasing when the radius is 1 cm? |
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Answer» Let r be the radius and V be the volume of the air bubble. Given ` (dr)/(dt) = 1/2 ` cm/sec Now, ` V= 4/3 pi r^(3)" "rArr (dV)/(dt) = 4 pi r^(2) (dr)/(dt)` at r = 1 cm ` (dV)/(dt) = 4 pi (1)^(2)* 1/2 = 2pi cm^(3)//sec` Therefore, the volume of bubble is increasing at the rate of ` 2pi cm^(3) //sec` |
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