Last updated on July 30th, 2025
A right circular cylinder is a 3-dimensional shape with two parallel circular bases connected by a curved surface. The surface area of the cylinder is the total area covered by its outer surface. The surface area of the cylinder includes both its curved surface and its circular bases. In this article, we will learn about the surface area of a right circular cylinder.
The surface area of a right circular cylinder is the total area occupied by the boundary or surface of the cylinder. It is measured in square units.
A cylinder is a 3D shape with two identical flat ends that are circular and a curved surface connecting them. The axis of the cylinder is the line joining the centers of the two bases.
The surface area of a cylinder can be divided into two parts: the curved surface area and the total surface area.
A cylinder has a curved surface, and it has two types of surface areas: the curved surface area and the total surface area. Look at the cylinder below to see its surface area, height (h), and radius (r).
A cylinder has two types of surface areas: Curved Surface Area of a Cylinder Total Surface Area of a Cylinder
The area of the curved part of the cylinder, excluding its bases, is known as the curved surface area of a cylinder.
The formula for the CSA (Curved Surface Area) of the cylinder is given as:
Curved Surface Area = 2πrh square units
Here, r is the radius of the base of the cylinder. h is the height of the cylinder.
The total area occupied by the cylinder, including the area of the curved surface and the area of the circular bases, is known as the total surface area of the cylinder.
The total surface area of a cylinder is calculated by using the formula: Total surface area = 2πr(r + h) square unit Where r is the radius of the base of the cylinder. h is the height of the cylinder.
Derivation of the Total Surface Area of a Cylinder
To find the total surface area of a cylinder, imagine unrolling the curved surface into a rectangle. The width of the rectangle is equal to the circumference of the base, and the height of the rectangle is the height of the cylinder.
The total surface area of a cylinder = base area of the cylinder + curved surface area of the cylinder.
Here, the base area of a cylinder = πr² Curved surface area of a cylinder = 2πrh
Substituting the formulas into the total surface area, Total surface area of a cylinder, T = 2πr² + 2πrh
Take the common terms out: T = 2πr(r + h)
Therefore, the total surface area of the cylinder T = 2πr(r + h)
The volume of a cylinder shows how much space is inside it. It tells us how much space is inside the cylinder or how much it can hold.
The volume of a cylinder can be found by using the formula: Volume = πr²h (cubic unit)
Students assume that the curved surface area (CSA) and the total surface area (TSA) of a cylinder are the same. This confusion arises because both involve the height and the radius.
Always remember that CSA is used on only the curved side of the cylinder, and TSA includes the curved surface and the bases.
Given r = 6 cm, h = 12 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 6 × 12 = 452.16 cm²
Find the total surface area of a cylinder with a radius of 4 cm and a height of 10 cm.
TSA = 351.68 cm²
Use the formula: TSA = 2πr(r + h) = 2 × 3.14 × 4 × (4 + 10) = 2 × 3.14 × 4 × 14 = 351.68 cm²
A cylinder has a radius of 5 cm and a height of 15 cm. Find the total surface area.
TSA = 628 cm²
Use the TSA formula: TSA = 2πr(r + h) = 2 × 3.14 × 5 × (5 + 15) = 2 × 3.14 × 5 × 20 = 628 cm²
Find the curved surface area of a cylinder with a radius of 3 cm and a height of 8 cm.
CSA = 150.72 cm²
CSA = 2πrh = 2 × 3.14 × 3 × 8 = 150.72 cm²
The height of a cylinder is 10 cm, and its curved surface area is 314 cm². Find the radius.
Radius = 5 cm
Students often make mistakes while calculating the surface area of a cylinder, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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