Q9 of 168 Page 197

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

Let V be the volume of the sphere, then


Therefore, Rate of change of volume (V) with respect to its radius (r) is given by,


…….. by chain rule


Thus, when r = 10cm


Then,


Therefore, the rate at which its volume is increasing with the radius when the later is 10 cm is 400π cm3/s.


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