# Surface Area of a Cylinder

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The surface area of a cylinder is the combined area of all the sides of the cylinder put together.

## To calculator the surface area of a cylinder, use the formula:

A = 2πr^2 + 2πrh

Where A is the area of the surface, r is the radius of the cylinder base, and h is the cylinder height.

In the above formula, the term, 2πr^2, calculates the sum of the areas of the two circular bases on two sides. The 2πrh is for the cylinder’s lateral surface area, that is the area of the curved lateral surface.

As an example, if the radius of the cylinder base is 5 cm and the cylinder height is 10 cm, the area of the surface would be:

A = 2π(5 cm)^2 + 2π(5 cm)(10 cm) = 50π cm^2 + 100π cm^2 = 150π cm^2 ≈ 471.2 cm^2

The lateral surface area of a cylinder is the area of the curved lateral surface and can be calculated using the formula:

A = 2πrh

In which A is the area of the lateral surface, r is the radius of the cylinder base, and h is the cylinder height.

As an example, if the radius of the cylinder base is 5 cm and the cylinder height is 10 cm, the area of the lateral surface would be:

A = 2π(5 cm)(10 cm) = 100π cm^2 ≈ 314.2 cm^2