The radius of an air bubble is increasing at the rate of . At what rate is the volume of the bubble increasing when the radius is 1 cm?

As, the air bubble is in the shape of a sphere.

Therefore, V be the volume of the sphere, then



Therefore, Rate of change of volume (V) with respect to time (t) is given by,


…….. by chain rule


It is given that



when, r = 1cm


Then,


Therefore, the rate is the volume of the bubble increasing when the radius is 1 cm is 2πcm3/s.


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