Answer :
SOLUTION
From the question,the radius and the height are equal, Hence
[tex]\begin{gathered} r=h \\ surfaceArea=64\pi in^2 \end{gathered}[/tex]The formula for surface area is
[tex]\begin{gathered} \text{Surface Area=2}\pi r^2+2\pi rh \\ \end{gathered}[/tex]Since
[tex]\begin{gathered} r=h \\ \text{Surface Area=2}\pi r^2+2\pi r(r)=2\pi r^2+2\pi r^2=4\pi r^2 \\ \text{Hence } \\ \text{surface Area=4}\pi r^2 \end{gathered}[/tex]Equate the formula to the surface Area to find the value of r
[tex]\begin{gathered} \text{surface Area=4}\pi r^2 \\ 64\pi=4\pi r^2 \\ \text{divide both sides by 4}\pi,\text{ we have } \\ \frac{64\pi}{4\pi}=\frac{4\pi r^2}{4\pi} \\ 16=r^2 \\ \text{taking square root of both sides, } \\ r=\sqrt[]{16} \\ r=4in \end{gathered}[/tex]hence
r= 4 inches
Then the volume of the cylinder will be;
[tex]\begin{gathered} \text{volume = }\pi r^2h \\ \text{Where r=h=4} \end{gathered}[/tex]Substitute the value of r, we have
[tex]\begin{gathered} \text{Volume}=\pi4^2(4) \\ \text{volume}=64\pi in^3 \end{gathered}[/tex]Hence
The volume of the cylinder will be 64π in³