Step-by-step explanation:
To find the exact surface area of the cylinder, we need to calculate the areas of the two circular bases and the lateral surface area (the curved surface).
1. Area of each circular base:
Area_base = π * r^2
2. Lateral surface area:
Area_lateral = 2 * π * r * h
3. Total surface area:
Total_area = 2 * Area_base + Area_lateral
Given:
- Radius (r) = 3 cm
- Height (h) = 5 cm
Let's calculate:
1. Area of each circular base:
Area_base = π * (3 cm)^2 = π * 9 cm^2
2. Lateral surface area:
Area_lateral = 2 * π * (3 cm) * (5 cm) = 30π cm^2
3. Total surface area:
Total_area = 2 * π * 9 cm^2 + 30π cm^2
= 18π cm^2 + 30π cm^2
= 48π cm^2
So, the exact surface area of the cylinder is 48π square centimeters.
