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.

Given: the radius of a spherical soap bubble is increasing at the rate of 0.2 cm/sec.

To find rate of increase of its surface area, when the radius is 7 cm

Let the radius of the given spherical soap bubble be r cm at any instant time.

Then according to the given criteria,

Rate of radius of the spherical soap bubble is increasing is,

Then the surface area of the spherical soap bubble at any time t will be

S = 4r² cm².

Applying derivative with respect to time on both sides we get,

[from equation(i)]

So when the radius is 7cm, the rate of surface area will become,

Hence the rate of increase of its surface area, when the radius is 7 cm is 11.2 cm²/sec