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.
The surface area of a cylinder has various real-world applications, such as calculating the amount of material needed to make a cylindrical container, determining the surface area of pipes and tubes used in plumbing, etc. 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.
What is the Surface Area of a Cylinder?
The surface area of a cylinder refers to the total area that the cylinder's curved surface and circular bases cover. The total surface area of the cylinder includes the area of the 2 bases of the cylinder (each of which is 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.
Surface Area of a Cylinder Formula
The formula for the surface area of the cylinder is used to find the 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 the total surface area. This means that a cylinder has two kinds of surface areas -Total Surface Area (TSA) and Curved Surface Area (CSA). For a cylinder whose base radius is 'r' and height is 'h':
- TSA of cylinder = 2πr2 + 2πrh (or) 2πr (r + h)
- CSA of cylinder = 2πrh
Have you noticed one thing in common in both formulas? Yes, that is 2πrh. Since TSA = CSA + 2 (area of two circles), we have TSA = 2πrh + 2 (πr2 ). Let us see how these formulas are derived in detail in the upcoming sections.
Total Surface Area of Cylinder (TSA)
The total surface area of the cylinder (TSA of cylinder) is obtained by adding the area of the two bases and the area of the curved surface. Consider a cylinder whose base has a radius 'r' and height of the cylinder is 'h'. 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.
- We know that the area of each base (circle) has an area of πr2.
- But how to find the area of the curved surface? For this, let us try a small experiment. Take a coke tin and cut its top and bottom (we are cutting as we are just finding the "curved" surface area) faces. Then cut the remaining cylindrical part vertically (height-wise) and open it. We can see that the cylindrical shape is turned into a rectangle. We need to find its length and width. Its width is nothing but the height of the cylinder 'h' and its length is the circumference of the base which is 2πr (to observe this, just close the rectangle back to the cylinder). Then the area of a rectangle is nothing but the area of the curved surface which is length × width = 2πr × h = 2πrh. Thus, the curved surface area of cylinder = 2πrh.
Thus, the total surface area of the cylinder (TSA) = πr2 + πr2 + 2πrh = 2πr2 + 2πrh = 2πr (r + h).
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).
By substituting the values of r = 5, h = 8, we get:
TSA = 2πr(r + h) = 2πr(r + h) = 2 × 3.14 × 5(5 + 8) = 408.41 cm2
The more detailed and geometrical derivation of TSA of a cylinder is below.
TSA of Cylinder Formula
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)
Curved Surface Area of Cylinder (CSA)
The curved surface area (CSA) 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:
CSA of Cylinder Formula
Curved surface of cylinder (or) CSA of cylinder = 2πrh
where,
- r = radius of the cylinder
- h = height of cylinder
- π = 22/7 or 3.14
The formula of CSA of cylinder has already been derived in the previous section.
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.
By substituting the values of r = 7, h = 14, we get: CSA = 2πrh = 2 × 3.14 × 7 × 14 = 615.8 cm2.
Differences Between TSA and CSA of Cylinder
The main difference between the Total Surface Area (TSA) and the Curved Surface Area (CSA) of a Cylinder is that TSA is the sum of the areas of all the surfaces of the cylinder, including the two circular bases and the curved surface, while CSA is the area of the curved surface only. The following table best summarizes the differences between TSA and CSA of a cylinder.
| Property | TSA of Cylinder | CSA of Cylinder |
|---|---|---|
| Definition | The sum of the areas of all the surfaces of the cylinder, including the two circular bases and the curved surface. | The area of the curved surface of the cylinder, excluding the areas of the two circular bases. |
| Formula | 2πr (r + h) | 2πrh |
| Application | TSA is used to determine the amount of material needed to make a cylindrical container. | CSA is used to determine the amount of wrapping paper needed to wrap a cylindrical gift. |
| Relationship | TSA includes CSA (and the two circular bases). | CSA is a part of TSA. Hence CSA is less than TSA. |
| Example | If r = 6 and h = 11, then total surface area is 2π(6)(6+11) = 640.88 square units. | If r = 6 and h = 11, then curved surface area is 2π(6)(11) = 414.69 square units. |
How to Calculate the SA of a Cylinder?
The surface area of a cylinder is equal to the 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. By 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
- Volume of Cylinder
- Right Circular Cylinder
- Difference Between Area and Surface Area
- Area of a Cylinder Calculator
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FAQs on Surface Area of Cylinder
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.
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 = πr2 + 2πrh = πr(r + 2h), 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 Total Surface Area of a Cylinder Formula?
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:
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 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)
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.
What will be the CSA of a Cylinder with 7 m Radius and 10 m Height?
The curved surface area of a cylinder can be calculated using the formula, CSA of cylinder = 2πrh. By substituting the values in this formula where r = 7, h = 10, we get, curved surface area of cylinder = 2πrh = 2 × 3.14 × 7 × 10 = 439.6 m2