Answer:
150.72 in²
Step-by-step explanation:
To find the surface area of the cylindrical sealed mailing tube, we can use the formula for the surface area of a cylinder:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Surface Area of a Cylinder}}\\\\SA=2\pi rh+2\pi r^2\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$SA$ is the surface area.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius of the circular base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
Given values:
- r = 2 in
- h = 10 in
- π = 3.14
Substitute the given values into the formula and solve for SA:
[tex]SA=2\cdot 3.14 \cdot 2 \cdot 10+2 \cdot 3.14 \cdot 2^2\\\\SA=2\cdot 3.14 \cdot 2 \cdot 10+2 \cdot 3.14 \cdot 4\\\\SA=6.28 \cdot 2 \cdot 10+6.28 \cdot 4\\\\SA=12.56 \cdot 10+25.12\\\\SA=125.6+25.12\\\\SA=150.72\; \sf in^2[/tex]
Therefore, the surface area of the sealed mailing tube is:
[tex]\LARGE\boxed{\boxed{150.72\; \sf in^2}}[/tex]
