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The surface area of a cylinder

Surface area of a cylinder - Calculator, Types, and Total surface area of the cylinder

A cylinder is a 3-dimensional shape having a curved body and circular bases on either end. Since it is curved in the middle and has circular bases, it does not have any vertices.
The surface area of a cylinder is defined as the total area occupied by its curved face and circular bases in space.

The surface area of a cylinder

The cylinder has two components:

  1. Curved body- The curved body of a cylinder is actually a rectangle that has a certain length and breadth. The rectangle, when folded along its breadth, gains height. Therefore, the height of a cylinder is actually the length of the rectangle, which is converted into a cylinder.
  2. Circular bases- The circular bases of a cylinder are present at both the ends of the cylinder. These are flat and circular in shape. In general, the circular bases are circles that are joined at either end of the curved body of the cylinder to obtain its ideal shape. Since the boundary of the circular bases is the same as the breadth of the rectangle turned curved part of the cylinder, the circle's circumference becomes equal to the breadth of the rectangle.

Types of surface areas of the cylinder

On the basis of the involvement of parts of the cylinder, the surface area of the cylinder can be calculated using different formulas as below:

  • Curved surface area or lateral surface area of the cylinder(CSA or LSA)
    The curved surface area or lateral surface area of a cylinder is the area occupied by the curved body of the cylinder. It does not involve the area of the circular bases of the cylinder. However, the circumference of the circular bases is equal to the circular folding of the cylinder. It is defined as the product of the height of the cylinder and the perimeter of its circular base. Therefore, the curved surface area of a cylinder is calculated by the following formula:

    The curved surface area of cylinder = h * 2πr
    The curved surface area of cylinder = 2πrh

    Where
    ‘h’ is the height of the cylinder, and
    ‘r’ is the radius of the circular bottom of the cylinder.

  • Surface area or total surface area of the cylinder(TSA)
    The total surface area of a cylinder involves all the parts of the cylinder. Unlike the lateral surface area, the total surface area involves the area of the curved body of the cylinder and the areas of both the circular bases on the ends of the cylinder. The total surface area of a cylinder is obtained by adding the lateral surface area and the area of the circular bases of the cylinder. Thus, the total surface area of the cylinder can be calculated by the following formula:

    The total surface area of cylinder = lateral surface area of cylinder + 2 * area of the circular base Total surface area of cylinder = 2πrh + 2πr²

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