The surface area of the cylinder = lateral area + 2 base area
Since the surface area = 325 in^2
Since the lateral area = 200 in^2
Subtract them to find 2 base area
2 base area = 325 - 200 = 125
Divide it by 2 to find the base area
[tex]\begin{gathered} b\mathrm{}A=\frac{125}{2} \\ b\mathrm{}A=62.5 \end{gathered}[/tex]Since the base of the cylinder is a circle
Since the area of the circle is
[tex]b\mathrm{}A=\pi\times r^2[/tex]Substitute bA by 62.5
[tex]62.5=\pi\times r^2[/tex]Divide both sides by pi
[tex]\frac{62.5}{\pi}=r^2[/tex]Take a square root for both sides
[tex]\begin{gathered} \sqrt[]{\frac{62.5}{\pi}}=r \\ r=4.46031092 \end{gathered}[/tex]Round it to the nearest tenth
r = 4.5 inches
