To find the surface area of a cylinder, we can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius
- \( h \) is the height
- The first term, \( 2\pi r^2 \), represents the area of the two circular bases.
- The second term, \( 2\pi rh \), represents the lateral surface area.
Given:
- Radius \( r = 4 \) mm
- Height \( h = 3 \) mm
- Use \( \pi = 3.14 \)
Now, let's calculate the surface area step by step.
-
Calculate the area of the two bases: \[ 2\pi r^2 = 2 \times 3.14 \times (4)^2 = 2 \times 3.14 \times 16 = 100.48 \text{ mm}^2 \]
-
Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 4 \times 3 = 2 \times 3.14 \times 12 = 75.36 \text{ mm}^2 \]
-
Add both areas together: \[ \text{Surface Area} = 100.48 + 75.36 = 175.84 \text{ mm}^2 \]
Therefore, the surface area of the cylinder is 175.84 mm².