#### To determine

**To find:** The rate of increase the surface area of the balloon of radius 1 ft.

#### Answer

The rate of increase of surface area of the balloon of radius 1 ft is, s′(1)=8π ft2/ft.

#### Explanation

Surface area of the balloon is, s=4πr2.

The rate of change of the balloon with respect to its radius is, s′(r)=8πr.

The rate of increase of surface area of radius 1 ft is,

s′(1)=8π(1)=8π ft2/ft.

The rate of increase of the surface area of the balloon of radius 1 ft is, s′(1)=8π ft2/ft.

#### To determine

**To find:** The rate of increase the surface area of the balloon of radius 2 ft.

#### Answer

The rate of increase of surface area of the balloon of radius 2 ft is, s′(2)=16π ft2/ft.

#### Explanation

Surface area of the balloon is, s=4πr2.

The rate of change of the balloon with respect to its radius is, s′(r)=8πr.

The rate of increase of surface area of radius 2 ft is,

s′(1)=8π(2)=16π ft2/ft.

Therefore, the rate of increase of the surface area of the balloon of radius 2 ft is, s′(2)=16π ft2/ft.

#### To determine

**To find:** The rate of increase the surface area of the balloon of radius 3 ft. What can be concluded from the parts (a), (b) and (c)?

#### Answer

The rate of increase of surface area of the balloon of radius 3 ft is, s(3)=24π ft2/ft.

#### Explanation

Surface area of the balloon is, s=4πr2.

The rate of change of the balloon with respect to its radius is, s′(r)=8πr.

The rate of increase of surface area of radius 3 ft is,

s′(1)=8π(3)=24π ft2/ft.

The rate of increase of the surface area of the balloon of radius 3 ft is, s(3)=24π ft2/ft.

Thus, the value of the rate of increase of surface area increases as the radius increases.

From the parts (a), (b) and (c), it can be concluded that the rate of change increases as radius increases.