Answer:
2.24π m²
Step-by-step explanation:
The formula for the surface area of a cylinder is:
[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]
The radius of a circle is half its diameter. So, in this case:
- [tex]r = 0.8\;\sf m[/tex]
- [tex]h = 0.6\;\sf m[/tex]
Substitute the values into the formula and solve for SA:
[tex]\begin{aligned}SA&=2\pi \cdot 0.8 \cdot 0.6+2\pi \cdot 0.8^2\\\\SA&=2\pi \cdot 0.8 \cdot 0.6+2\pi \cdot 0.64\\\\SA&=0.96\pi +1.28\pi\\\\SA&=2.24\pi\; \sf m^2\end{aligned}[/tex]
Therefore, the exact surface area of the cylinder is:
[tex]\Large\boxed{\boxed{2.24\pi \; \sf m^2}}[/tex]
