103 LearnersLast updated on August 29, 2025
Surface Area of Cylinders and Prisms
Cylinders and prisms are 3-dimensional shapes with flat bases and uniform cross-sections. The surface area of these shapes is the total area covered by their outer surfaces. This includes both the lateral or curved surfaces and the bases. In this article, we will learn about the surface area of cylinders and prisms.
What is the Surface Area of a Cylinder and a Prism?
The surface area of a cylinder and a prism is the total area occupied by their outer surfaces. It is measured in square units. A cylinder has two parallel circular bases and a curved surface connecting them, while a prism has two parallel polygonal bases and rectangular sides.
Both shapes have a lateral surface area and a total surface area. Cylinders and prisms can vary in shape, such as right circular cylinders, rectangular prisms, and oblique cylinders or prisms, based on the alignment of their sides with respect to the bases.
Surface Area of a Cylinder and Prism Formula
Both cylinders and prisms have lateral surface areas and total surface areas.
The formulas depend on the specific dimensions of the shape such as height, radius (for cylinders), and side lengths (for prisms).
For a cylinder: Curved Surface Area (CSA): 2πrh
Total Surface Area (TSA): 2πr(h + r)
For a rectangular prism: Lateral Surface Area: 2h(l + w)
Total Surface Area: 2(lw + lh + wh)
Curved Surface Area of a Cylinder
The curved surface area of a cylinder is the area of the side surface that wraps around the cylinder, excluding the bases.
The formula for the curved surface area of a cylinder is given as: Curved Surface Area = 2πrh square units
Here, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Total Surface Area of a Cylinder
The total surface area of a cylinder includes both the curved surface area and the area of its circular bases.
The total surface area of a cylinder is calculated using the formula:
Total Surface Area = 2πr(h + r) square units Where r is the radius of the base, and h is the height of the cylinder.
To derive this, consider the cylinder as having two circular bases and a curved surface:
Total surface area = area of the two bases + curved surface area
Here, the area of each base = πr²
Curved surface area = 2πrh
Thus, the total surface area = 2πr² + 2πrh
Taking common terms out: TSA = 2πr(h + r)
Volume of a Cylinder
The volume of a cylinder shows how much space is enclosed within it. It can be calculated using the formula: Volume = πr²h cubic units Here, r is the radius of the base, and h is the height of the cylinder.
Confusion between Lateral and Total Surface Area
Students assume that the lateral surface area and the total surface area are the same. This confusion arises because both involve the height and the bases. Always remember that the lateral surface area is only the side surface, while the total surface area includes the bases.
Mistake 1
Using Incorrect Dimensions
Some students mistakenly use the wrong dimensions, such as using diameter instead of radius for cylinders or incorrect side lengths for prisms. Always double-check the given dimensions before using them in formulas.
Mistake 2
Using the Wrong Value for π
A common mistake is using an incorrect value for π. Use accurate values like 22/7 or 3.14 for calculations involving circles.
Mistake 3
Forgetting to Include Both Bases in Total Surface Area
Students often calculate only the lateral surface area and forget to add the areas of the two bases. Always include both parts when calculating the total surface area.
Mistake 4
Assuming All Prisms Are Rectangular
Some students mistakenly believe that all prisms are rectangular, but prisms can have different polygonal bases. Ensure to use the correct formula based on the shape of the base.
Mistake 5
Solved Examples of Surface Area of Cylinders and Prisms
Find the curved surface area of a cylinder with a radius of 4 cm and a height of 9 cm.
CSA = 226.08 cm²
Problem 1
Given r = 4 cm, h = 9 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 4 × 9 = 226.08 cm²
Find the total surface area of a cylinder with a radius of 6 cm and a height of 5 cm.
Explanation
TSA = 414.48 cm²
Problem 2
Use the formula: TSA = 2πr(h + r) = 2 × 3.14 × 6 × (5 + 6) = 2 × 3.14 × 6 × 11 = 414.48 cm²
A rectangular prism has a length of 8 cm, a width of 3 cm, and a height of 10 cm. Find the total surface area.
Explanation
TSA = 276 cm²
Problem 3
Use the formula: TSA = 2(lw + lh + wh) = 2(8 × 3 + 8 × 10 + 3 × 10) = 2(24 + 80 + 30) = 2 × 134 = 268 cm²
Find the lateral surface area of a rectangular prism with a length of 7 cm, a width of 5 cm, and a height of 12 cm.
Explanation
LSA = 288 cm²
Problem 4
LSA = 2h(l + w) = 2 × 12 × (7 + 5) = 2 × 12 × 12 = 288 cm²
The total surface area of a cylinder is 376.8 cm² with a height of 6 cm.
Find the radius if the total surface area formula is 2πr(h + r).
Explanation
Radius = 4 cm
It is the total area that covers the outside of the cylinder, including its curved surface and the two bases.
1.What are the two types of surface area in a cylinder?
2.What is the difference between a prism and a cylinder?
3.Is the curved surface area the same as the lateral surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of Cylinders and Prisms
Students often make mistakes while calculating the surface area of cylinders and prisms, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
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.
Fun Fact
: She has songs for each table which helps her to remember the tables
