Answer:
490.1 cm²
Step-by-step explanation:
The lateral surface area ([tex]A_{\textsf{Lateral}}[/tex]) of a cylinder is given by the formula:
[tex] \Large\boxed{\boxed{A_{\textsf{Lateral}} = 2\pi rh}} [/tex]
where
- [tex] r [/tex] is the radius and
- [tex] h [/tex] is the height.
Given that [tex] r = 6 [/tex] cm and [tex] h = 13 [/tex] cm, substitute these values into the formula:
[tex] A_{\textsf{Lateral}} = 2\pi \times 6 \times 13 [/tex]
[tex] A_{\textsf{Lateral}} = 156\pi [/tex]
[tex] A_{\textsf{Lateral}} \approx 156 \times 3.14159265359 [/tex]
[tex] A_{\textsf{Lateral}} \approx 490.08845396004 [/tex]
[tex] A_{\textsf{Lateral}} \approx 490.1 \textsf{(in nearest tenth)}[/tex]
So, the lateral surface area of the cylinder is approximately [tex] 490.1 [/tex] square centimeters rounded to the nearest tenth.
