Question

A spherical balloon has a 22-inch diameter when it's fully inflated. Half of the air is let out but remains sphere-shaped.

a.) find the volume of the fully inflated balloon.

b.) find the volume of the half inflated balloon.

c.) whats the radius of the half inflated balloon rounded to the nearest tenth?

Answer 1

a) 5572.45 cubic inches

b) 2786.23 cubic inches

c) 8.7 inches

Explanation:

We are given the following in the question:

Diameter of spherical balloon = 22 inch.

Thus,

Radius of spherical balloon, r = 11 inch

a) volume of the fully inflated balloon.

Volume of balloon = Volume of sphere

`V=(4)/(3)\pi r^3`

Putting value, we get,

`V = (4)/(3)* 3.14* (11)^3 = 5572.45\text{ cubic inches}`

The volume of fully inflated balloon is 5572.45 cubic inches.

b) volume of the half inflated balloon.

`V' = (1)/(2)V\\\\V' = (1)/(2)* 5572.45\\\\V' = 2786.225\approx 2786.23\text{ cubic inches}`

The volume of half inflated balloon is 2786.23 cubic inches.

c) Radius of half inflated balloons

`V=(4)/(3)\pi r^3`

Putting values, we get

`2786.23 =(4)/(3)* 3.14* r^3\\\\r^3 = (2786.23* 3)/(4* 3.14)\\\\r^3 = 665.5\\\Rightarrow r = 8.73\approx 8.7\text{ inches}`

Thus, the radius of half inflated balloon is 8.7 inches