The formula for the total surface area of a cylinder is given by:
\[ \text{Total Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to 3.14159.
This formula includes the area of the two circular bases (the top and bottom) and the lateral surface area (the side).
To break it down:
- The area of the two circular bases (top and bottom) is \( 2\pi r^2 \).
- The lateral surface area is \( 2\pi rh \).
Combining these gives the total surface area formula.