Question

The volume of gas a balloon can hold varies directly as the cube of its radius. Imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. How many cubic inches of gas must be released to reduce the radius down to 2 inches?

Answer 1

Answer: 57 in³

Explanation:

1. You know that the volume (V) of gas a balloon can hold varies directly as the cube of its radius (r). Then, you can write the following expression:

`V=kr^(3)`

Where k is the constant of proportionality.

2. You can calculate k as following:

`k=(V_1)/(r^(3))\\k=(81in^(3))/((3in)^(3))\\k=3`

3. Then, to calculate the cubic inches that must be released to reduce the radius down to 2 inches:

- Solve for the volume as following:

`V_2=3(2in)^(3)=24in^(3)`

- Make the subtraction of the two volumes shown above. Then, the result is:

`V_3=81in^(3)-24in^(3)=57in^(3)`