The radius of a spherical soap bubble is increasing at the rate of 0.2 cm/sec. Find the rate of increase of its surface area, when the radius is 7 cm.

Explanation

Surface area of the spherical bubble `(S) = 4pir^2`

Here, `r = 7cm and (dr)/dt = 0.2` cm/sec

Now, `S = 4pir^2`

`:. (dS)/dt = 8pir((dr)/dt)`

`=> (dS)/dt = 8pi(7)(0.2) = 11.2pi`

So, rate of change of surface area will be `11.2pi (cm^2)/sec`.