A weather balloon was filled with gas until its diameter was 5 ft. After reaching its highest altitude in the atmosphere, the balloon burst, with a diameter of 28 ft. What is the difference in volume of the balloon when it burst compared to at launch?

Step-by-step explanation:

The balloon is spherical in shape. The formula for determining the volume of a sphere is expressed as

Volume = 4/3 × πr³

Where

At represents the radius of the sphere.

π is a constant whose value is 3.14

The diameter of the balloon before it was launched is 5 feet

Radius = diameter/2

r = 5/2 = 2.5

Therefore, volume at launch is

4/3 × 3.14 × 2.5³

= 65.42 ft³

When the balloon burst, the diameter is 28 ft

Radius = 28/2 = 14 ft

Therefore, volume when it burst is

4/3 × 3.14 × 14³

= 11488.2 ft³

The difference in volume of the balloon when it burst compared to at launch is

11488.2 - 65.42 = 11422.78 ft³

the first option is the answer.