The radius of an air bubble is increasing at the rate of 0.5 cm/sec. At what rate is the volume of the bubble increasing when the radius is 1 cm?

Explanation

The air bubble is in the shape of a sphere.
Now, the volume of an air bubble `(V)` with radius `(r)` is given by,

`V=4/3pir^3`

The rate of change of volume `(V)` with respect to time `(t)` is given by,

`(dV)/dt=4/3pid/(dr)(r^3)xx(dr)/dt4/3pi(3r^2)xx(dr)/dt`

`implies(dV)/dt=4pir^2(dr)/dt`

It is given that `(dr)/(dt)=1/2``(cm)/s`

Therefore, when `r=1` cm,

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