The surface area , where  is radius of spherical balloon.

(a)

Rate of increase in surface area when  ft:

Consider .

Differentiate on each side with respect to  sides.

.

Substitute  in above expression.

 ft²/ft.

(b)

The rate of increase of surface area when .

ft² /ft.

(c)

The rate of increase of surface area when .

ft² /ft.

Conclusion :

The rate increases as the radius increases.

(a)  .

(b)  .

(c)  .

The rate increases as the radius increases.