Surface Area of Cylinder

The surface area of a cylinder can be defined as the total space covered by the flat surfaces of the bases of the cylinder and its curved surface. The total surface area of the cylinder has two components - a curved surface area and two flat surface areas.

Let us learn more about what is the surface area of the cylinder and how to calculate the total surface area and the lateral surface area of a cylinder.

The surface area of a cylinder can be defined as the amount of space covered by the flat surface of the bases of the cylinder and the curved surface of the cylinder. The total surface area of the cylinder includes the area of the 2 bases of the cylinder which are in the shape of a circle and the area of the curved surface. Surface area is expressed in square units like square centimeters, square inches, square feet, and so on. A cylinder is a 3-D solid object which consists of two circular bases connected with a curved face. Observe the figure given below which shows the different parts of a cylinder that are used to find the surface area of a cylinder.

The formula for the surface area of the cylinder is used to find the surface area occupied by the bases of the cylinder and the curved surface of the cylinder. Since a cylinder has a curved surface, we can express its curved surface area as well as total surface area. This means that a cylinder has two kinds of surface areas -Total Surface Area (TSA) and Curved Surface Area (TSA).

The curved surface area of a cylinder is the surface area covered by its curved surface only. If the radius of the base of the cylinder is 'r' and the height of the cylinder is 'h', the curved surface area of a cylinder is calculated using the following formula:

Curved Surface Area of Cylinder Formula

Curved surface area of cylinder = 2πrh

where,

• r = radius of the cylinder
• h = height of cylinder
• π = 22/7 or 3.14

Example: Find the Curved surface area of a cylinder of radius 7 cm and height 14 cm.

Solution: The curved surface area of a cylinder can be calculated using the formula, CSA = 2πrh. After substituting the value of r = 7, h = 14, we get: CSA = 2πrh = 2 × 3.14 × 7 × 14 = 615.8 cm²

The total surface area of the cylinder is obtained by adding the area of the two bases and the area of the curved surface. Thus, the formula for the total surface area of the cylinder is given as,

Total surface area of cylinder = Area of two bases + Area of the curved surface. Since the bases of the cylinder are circular in shape, their combined area will be πr² + πr². We already know that the curved surface area of a cylinder is 2πrh.

Total surface area of cylinder ⇒ (πr² + πr²) + 2πrh

⇒ 2πr² + 2πrh

Total surface area of cylinder = 2πr(r+h)

where,

• r = radius of the cylinder
• h = height of cylinder

Example: Find the Total surface area (TSA) of a cylinder of radius 5 cm and height 8 cm.

Solution: The Total surface area (TSA) of a cylinder can be calculated using the formula, TSA = 2πr(r + h). After substituting the value of r = 5, h = 8, we get: TSA = 2πr(r + h) = 2πr(r + h) = 2 × 3.14 × 5(5 + 8) = 615.8 cm²

Derivation of the Formula for the Surface Area of Cylinder

The area of any shape is the space occupied by it. A cylinder has 2 flat surfaces which are circles and a curved surface that opens up as a rectangle. Consider the cylinder given below whose height is 'h' and radius is 'r'. Let us open a cylinder in the 2-dimensional form and understand this.

Observe the figure given above in which the area of the curved surface opens up as a rectangle and the two bases are circles.

• Now, the area of the two circles is (πr² + πr²) whose base radius is 'r'.
• In the rectangle, one side is the height of the cylinder h, while the length of this rectangle is the circumference of the circle, that is, 2πr.
• Thus, the area of this rectangle (l × b) is = 2πr × h = 2πrh which is also the curved surface area of the cylinder.
• Therefore, total surface area of the cylinder = 2πr² + 2πrh = 2πr(r + h)

The surface area of a cylinder is equal to the surface area occupied by the bases of the cylinder and the curved surface of the cylinder. Using the steps given below, let us find the total surface area of a cylinder which has a radius of 7 units and a height of 9 units.

• Step 1: Note the radius, 'r', and height, 'h' of the cylinder. Make sure both have the same units. Here, r = 7, h = 9
• Step 2: In the given question, we need to find the total surface area of the cylinder, so, we will use the formula for the total surface area of the cylinder, total surface area = 2πr(r + h)
• Step 3: Substitute the given values and give the answer in square units. After substituting the values in the formula we get, total surface area = 2πr(r + h) ⇒ 2π × 7(7 + 9) ⇒ 2π × 112 ⇒ 2 × 3.14 × 112 ⇒ 703.6 square units.

☛ Related Articles

• Surface Area of Cube
• Surface Area of Cuboid
• Surface Area of Prism
• Surface Area of Cone
• Surface Area of Sphere
• Difference Between Area and Surface Area

What is the Surface Area of a Cylinder?

The surface area of a cylinder is defined as the total area or region covered by the surface of the shape. Since a cylinder has 2 flat surfaces and 1 curved surface the total surface area includes the area of the flat surfaces and the area of the curved surface. The surface area of a cylinder is expressed in square units, like m², in², cm², yd², etc.

How to Find the Surface Area of a Cylinder?

The surface area of a cylinder can be found using the steps given below:

• Step 1: Note down the base radius, 'r', and height, 'h' of the cylinder. Check that the units of the dimensions are the same.
• Step 2: Apply the appropriate formula to find the surface area of a cylinder given as,
  Curved Surface Area of cylinder = 2πrh
  Total Surface Area of cylinder = 2πr(h + r)
• Step 3: Substitute the given values and express the answer in square units.

What is the Formula of Total Surface Area of a Cylinder?

The formula to calculate the total surface area of a cylinder is expressed as, total surface area of cylinder = 2πr(r + h). This total surface area includes the area of the 2 bases (2πr²) and the curved surface area (2πrh). Here 'r' is the radius and 'h' is the height of the cylinder.

☛Also Check:

• Surface Area Formulas
• Measurement Formulas

How to Find the Surface Area of an Open Top Cylinder?

The surface area of an open-top cylinder can be calculated by finding the area of one base and the curved surface. Thus, the area of a cylinder without a top can be expressed as, the surface area of an open-top cylinder = πr(2r + h), where 'r' is the radius and 'h' is the height of the cylinder. It should be noted that we have taken the area of one base because the cylinder does not have a top.

What is the Formula to Find the Base Area of a Cylinder?

The base of a cylinder is in the shape of a circle. Therefore, the formula to find the base area of a cylinder is expressed as, πr², where 'r' is the base radius of the cylinder. If the area of both the bases is required, then it will be, πr² + πr² = 2πr²

How to Calculate Surface Area of Cylinder Using Calculator?

The surface area of a cylinder can be easily determined using the 'surface area of cylinder calculator'. It is the fastest method with which we can evaluate the surface area within a few seconds. To use it, we need to enter the value of the specific parameters in the calculator screen such as the radius and the height of the cylinder. Try Cuemath's online surface area of cylinder calculator and get your answers just by a click. Check out surface area of cylinders worksheets for more practice.

How to Find the Curved Surface Area of a Cylinder?

The curved surface area of a cylinder is calculated using the formula, curved surface area of cylinder = 2πrh, where 'r' is the radius and 'h' is the height of the cylinder.

How to Find Surface Area of Cylinder with Diameter and Height?

If the diameter and height of the cylinder is given, we can find the surface area of the cylinder using the same formula. We can get the radius of the cylinder using the diameter since diameter = 2 × radius. After finding the radius, we can use the formula, Total Surface Area of cylinder = 2πr(r + h)

What will be the Curved Surface Area of a Cylinder with 7 m Radius and 10 m Height?

The curved surface area of a cylinder can be calculated using the formula, Curved surface area of cylinder = 2πrh; where, r = Radius of the cylinder and h = Height of the cylinder. After substituting the values in the formula where r = 7, h = 10, we get, Curved surface area of cylinder = 2πrh = 2 × 3.14 × 7 × 10 = 439.6 m²