Question

The radius of a spherical soap bubble increases @ 0.2 cm per second find the rate of increase of its surface area when the radius is 7 cm?

Answer 1

`11.2 pi \ cm^2 \s^(-1)`

Explanation:

The surface area is:

`S = 4 pi r^2`

Chain rules dictates that:

`(dS)/(dt) = (dS)/(dr) * (dr)/(dt)`

`= 8 pi r * 0.2 = 1.6 \ pi r`

`((dS)/(dt))_(r = 7 ) = 1.6 \ pi (7) = 11.2 pi \ cm^2 \s^(-1)`