136 LearnersLast updated on August 5th, 2025
Surface Area of Half Cylinder
A half cylinder is a 3-dimensional shape that resembles a cylinder cut in half lengthwise. The surface area of a half cylinder is the total area covered by its outer surface. The surface area of the half cylinder includes its curved surface, the rectangular base, and the semicircular base. In this article, we will learn about the surface area of a half cylinder.
What is the Surface Area of a Half Cylinder?
The surface area of a half cylinder is the total area occupied by the boundary or surface of a half cylinder. It is measured in square units.
A half cylinder is a 3D shape made by slicing a cylinder along its length. It has a semicircular base, a flat rectangular surface, and a curved surface.
The surface area is the sum of these three parts:
the curved surface area, the rectangular area, and the semicircular base area.
Half cylinders are often used in architectural designs and engineering projects for their aesthetic appeal and structural properties.
Surface Area of a Half Cylinder Formula
A half cylinder has a curved surface and two flat surfaces. It has three components for its surface area: the curved surface area, the rectangular base area, and the semicircular base area.
Look at the diagram of a half cylinder below to see its surface area, height(h), and radius(r).
A half cylinder has three types of surface areas:
Curved Surface Area of a Half Cylinder
Rectangular Surface Area of a Half Cylinder
Semicircular Base Area of a Half Cylinder
Curved Surface Area of a Half Cylinder
The area of the curved part of the half cylinder is known as the curved surface area. The formula for the CSA (Curved Surface Area) of the half cylinder is given as:
Curved Surface Area = πrh square units
Here, r is the radius of the base of the half cylinder. h is the height of the half cylinder.
Total Surface Area of a Half Cylinder
The total area occupied by the half cylinder, including the area of the curved surface, the rectangular surface, and the semicircular base, is known as the total surface area of the half cylinder.
The total surface area of a half cylinder is calculated by using the formula:
Total Surface Area = πrh + 2rh + ½πr² square units Where r is the radius of the base of the half cylinder. h is the height of the half cylinder.
Derivation of the Total Surface Area of a Half Cylinder
To find the total surface area of a half cylinder, imagine slicing it along its length and unfolding it. The curved surface forms a rectangle, the base is a semicircle, and there is a rectangular face.
Let us take a half cylinder with height(h) and radius of the base(r).
Total surface area of a half cylinder = curved surface area + rectangular base area + semicircular base area
Here, the curved surface area = πrh
Rectangular base area = 2rh
Semicircular base area = ½πr²
Adding these components gives: Total Surface Area = πrh + 2rh + ½πr²
Volume of a Half Cylinder
The volume of a half cylinder shows how much space is inside it. It tells us how much space is inside the half cylinder or how much it can hold. The volume of a half cylinder can be found by using the formula: Volume = ½(πr²h) cubic units
Confusion between the curved surface area and total surface area
Students assume that the curved surface area (CSA) and the total surface area (TSA) of a half cylinder are the same. This confusion arises because both involve the radius and height. Always remember that CSA is used only on the curved side of the half cylinder, and TSA includes the curved surface, the rectangular surface, and the semicircular base.
Mistake 1
Forgetting the rectangular base area
Some students mistakenly forget to add the area of the rectangular base when calculating the total surface area. Remember the formula includes this: Total Surface Area = πrh + 2rh + ½πr².
Mistake 2
Using the wrong value for π
A common mistake of students is using 22 as the value of π. Instead, use accurate values like 22/7 or 3.14. π is a special number in math, and using the correct value is important for getting the right answer.
Mistake 3
Incorrectly calculating the semicircular area
Students often calculate the semicircular area as if it were a full circle. Always remember that the semicircular area is half of the circular area: ½πr².
Mistake 4
Assuming curved surface area and lateral surface area are different
Some students mistakenly believe that curved surface area and lateral surface area are different, but in a half cylinder, they mean the same thing. So, use the same formula for both.
Mistake 5
Solved Examples of Surface Area of Half Cylinder
Find the curved surface area of a half cylinder with a radius of 4 cm and a height of 12 cm.
CSA = 150.72 cm²
Problem 1
Given r = 4 cm, h = 12 cm. Use the formula: CSA = πrh = 3.14 × 4 × 12 = 150.72 cm²
Find the total surface area of a half cylinder with radius 3 cm and height 10 cm.
Explanation
TSA = 188.4 cm²
Problem 2
Use the formula: TSA = πrh + 2rh + ½πr² = 3.14 × 3 × 10 + 2 × 3 × 10 + ½ × 3.14 × 3² = 94.2 + 60 + 14.13 = 188.4 cm²
A half cylinder has a radius of 5 cm and a height of 8 cm. Find the total surface area.
Explanation
TSA = 235.5 cm²
Problem 3
Use the TSA formula: TSA = πrh + 2rh + ½πr² = 3.14 × 5 × 8 + 2 × 5 × 8 + ½ × 3.14 × 5² = 125.6 + 80 + 39.25 = 235.5 cm²
Find the curved surface area of a half cylinder with radius 2.5 cm and height 7 cm.
Explanation
CSA = 55 cm²
Problem 4
CSA = πrh = 3.14 × 2.5 × 7 = 55 cm²
The height of a half cylinder is 15 cm, and its curved surface area is 330 cm². Find the radius.
Explanation
Radius = 7 cm
It is the total area that covers the outside of the half cylinder, including its curved surface, rectangular base, and semicircular base.
1.What components make up the surface area of a half cylinder?
2.Is the curved surface area the same as the lateral surface area?
3.What is the difference between radius and height in a half cylinder?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Half Cylinder
Students often make mistakes while calculating the surface area of a half cylinder, leading to incorrect answers. Below are some common mistakes and the ways to avoid them.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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: She has songs for each table which helps her to remember the tables
