Explanation
We are asked to find the volume of the sphere given that the diameter is 8ft
The formula to be used will be
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ \\ where \\ r=radius=\frac{diamter}{2}=\frac{8}{2}=4ft \end{gathered}[/tex]Therefore, the answer will be
[tex]\begin{gathered} v=\frac{4}{3}\times\pi\times4^3 \\ \\ v=268.1ft^3 \end{gathered}[/tex]Next
we are told that if the balloon is blown up with air
The diameter is 13 inches.
Therefore, the volume will be
[tex]radius=\frac{diameter}{2}=\frac{13inches}{2}=6.5inches[/tex]Hence
[tex]v=\frac{4}{3}\times\pi\times6.5^3=1150.3\text{ inches}^3[/tex]