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Home > News & Articles > Formula of CSA of Cylinder: Definition, Examples, Surface Area, Derivation, TSA, and Differentiation
Updated on 24th July, 2023 , 4 min read
The Surface Area of a Cylinder is classified into two types: Curved Surface Area (CSA) and Total Surface Area (TSA). In geometry, the area of any form is the area it occupies in a plane. A cylinder can have two surfaces: one with a curved surface and one with two round bases. The area of both circular bases is the same.
A cylinder is a three-dimensional solid structure with two parallel circular bases linked at a constant distance by a curving surface. It's also possible to see it as a stack of circular discs. The axis of the cylinder is the line segment connecting the centers of two circular bases. The distance from the axis to the outer curved surface is known as the cylinder's radius (r), and the perpendicular distance between the two parallel circular bases is known as the cylinder's height (h).
There are several instances of cylindrical-shaped items that we encounter in our daily lives which are as follows-
The area of any shape in geometry is the region it covers in a plane. A cylinder is made up of two types of surfaces: curved surfaces and circular bases. Both circular bases have the same area. The cylinder's surface area may be divided into two types-
A cylinder's curved surface area (CSA) is the area covered by its curved surface solely. The curved surface area of a cylinder is determined using the formula if the radius of the base of the cylinder is 'r' and the height of the cylinder is 'h'.
where,
r = radius of the cylinder
h = height of the cylinder
π = 22/7 or 3.14
Solution: CSA of cylinder = 2 𝜋rh
By placing the values,
r = 7 cm
h = 14cm
We get-
CSA = 2 𝜋rh
= 2 x 3.14 x 7 x 14
= 6.28 x 98 cm²
= 615.44 cm²
Therefore, the curved surface area of a cylinder is 615.44 cm².
The following is the derivation of the formula of CSA of a cylinder-
= 2πrh
A cylinder's total surface area is defined as the sum of the areas of its curving surface and two circular bases. TSA of a cylinder of radius 'r' and height 'h' is given by-
or,
Cylinder TSA = Cylinder CSA + area of its two circular bases
= 2rh + 2r²square units
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The primary distinction between the Total Surface Area (TSA) and Curved Surface Area (CSA) of a Cylinder is that TSA is the sum of the areas of all the cylinder's surfaces, including the two circular bases and the curved surface, whereas CSA is the area of the curved surface only. The following table gives the difference between curved surface area and the total surface area of a cylinder-
Particulars | CSA | TSA |
Definitions | The area of the cylinder's curved surface, omitting the regions of the two circular bases. | The total area of the cylinder's surfaces, including the two circular bases and the curving surface. |
Formula | 2πrh | 2πr (r + h) |
Example | r = 8, h = 3, Then the CSA is 2π (8) (3) = 150.72 square units. | r = 8, h = 3, Then the TSA is 2π (8) (8+3) = 404.92 square units. |
Application | The CSA formula is used to calculate the amount of wrapping paper required to wrap a cylindrical present. | TSA is used to calculate the quantity of material required to construct a cylindrical container. |
Relationship | The TSA includes the CSA. As a result, CSA is smaller than TSA. | TSA incorporates CSA (as well as the two circular bases). |
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. A cylinder is a three-dimensional form with two parallel circular bases linked by a curving surface.
Ans. The slant height is the height of a triangle with a lateral face.
Ans. The lateral surface area of a solid object is the region that encompasses all of its surface area except the base and top. Consider the four sides of a wall, excluding the ceiling and floor of the room. So the LSA of a cylinder is its area minus the top and bottom areas. Whereas "curved" implies something folded, a cylinder is a curved object, hence we should avoid using LSA in cylinders or cones. In this case, we utilized CSA to determine the location. Despite the fact that the technique is the same, we omit the top and bottom portions from the computation.
Ans. Curved Surface Area (CSA) and Total Surface Area (TSA) are the two types of Surface Area of a cylinder.
Ans. The CSA formula is used to calculate the amount of wrapping paper required to wrap a cylindrical present.
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