Answer:
314.159 km²
Step-by-step explanation:
To find the surface area of the cylinder, we need to calculate the area of the two circular bases and the lateral surface area.
Given:
Radius = 5 km
Height = 5 km
The formula for the surface area A of a cylinder is:
\(A = 2\pi r^2 + 2\pi rh\)\(A = 2\pi r^2 + 2\pi rh \\\)
Substituting the given values into the formula:
\(A = 2\pi (5 \text{ km})^2 + 2\pi (5 \text{ km})(5 \text{ km}) \\\\ A = 2\pi (25 \text{ km}^2) + 2\pi (25 \text{ km}^2) \\\\ A = 50\pi \text{ km}^2 + 50\pi \text{ km}^2 \\\\ A = 100\pi \text{ km}^2\)
Now, let's calculate the value of π:
\(\pi \approx 3.14159\)
So, the surface area of the cylinder is approximately:
\(A \approx 100 \times 3.14159 \text{ km}^2 \\\\ \approx 314.159 \text{ km}^2\)
