Surface Area of Cylinders

Surface Area of a Cylinder
The surface area of a cylinder is the total area of all its surfaces. A cylinder is a three-dimensional shape with two parallel and congruent circular bases and a curved side that connects them.

The following diagram gives the surface area formula for a cylinder. Scroll down the page for more examples and solutions.

 

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To understand and calculate the surface area, it’s helpful to imagine “unrolling” the cylinder into a net. When unrolled, a cylinder’s net consists of:
Two circles: These are the top and bottom bases.
One rectangle: This is the curved side that connects the two circular bases.

Formula for the Surface Area of a Cylinder
The total surface area (SA) of a closed cylinder is the sum of the areas of its two circular bases and the area of its curved (lateral) surface:
SA = (Area of 2 Circular Bases) + (Area of Curved Surface)

1. Area of the Two Circular Bases
   Each base is a circle. The combined area of the two circles (top and bottom) is given by 2πr², where r is the radius of the circle.
   
2. Area of the Curved Surface (Lateral Surface Area)
   If you unroll the curved surface of the cylinder, it forms a rectangle.
   The width of this rectangle is the height of the cylinder (h).
   The length of this rectangle is the circumference of the circular base, which is 2πr.
   The area of the curved surface = 2πrh
   

Combined Formula for Total Surface Area
Adding the areas of the bases and the curved surface, the total surface area of a cylinder is:
SA = 2πr² + 2πrh

GCSE Maths
Surface area of a cylinder
How to find the formula for surface area of a cylinder?

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Surface area of a cylinder
How to find the surface area of a cylinder given the radius and the height?

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Surface area of a cylinder
How to find the surface area of a cylinder without the top surface?

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