Answer: 57 in³
Step-by-step 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:
[tex]V=kr^{3}[/tex]
Where k is the constant of proportionality.
2. You can calculate k as following:
[tex]k=\frac{V_1}{r^{3}}\\k=\frac{81in^{3}}{(3in)^{3}}\\k=3[/tex]
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:
[tex]V_2=3(2in)^{3}=24in^{3}[/tex]
- Make the subtraction of the two volumes shown above. Then, the result is:
[tex]V_3=81in^{3}-24in^{3}=57in^{3}[/tex]
