106 LearnersLast updated on August 5th, 2025
Surface Area of Prisms and Cylinders
A prism or a cylinder is a 3-dimensional shape with flat faces or curved surfaces. The surface area of these shapes is the total area covered by their outer surfaces. The surface area for prisms includes the areas of all its faces, while for cylinders, it includes both the curved surface and the circular bases. In this article, we will learn about the surface area of prisms and cylinders.
What is the Surface Area of Prisms and Cylinders?
The surface area of prisms and cylinders is the total area occupied by the boundaries or surfaces of these shapes. It is measured in square units.
A prism is a 3D shape with two identical bases and flat sides, while a cylinder has a curved surface and two circular bases. Prisms can be classified into different types based on the shape of their base, such as rectangular prisms and triangular prisms. Cylinders are generally circular.
For prisms, surface area includes the areas of all its faces, while for cylinders, it includes the curved surface area and the total surface area.
Surface Area Formulas for Prisms and Cylinders
Prisms and cylinders have different surface area calculations based on their shapes: 1. Surface Area of Prisms 2. Surface Area of Cylinders
Surface Area of Prisms
The surface area of a prism is the sum of the areas of all its faces. For a rectangular prism, the surface area is calculated as:
Surface Area = 2lw + 2lh + 2wh square units
Where l is the length, w is the width, and h is the height of the prism.
Surface Area of Cylinders
The total area occupied by the cylinder, including the area of the curved surface and the area of the two circular bases, is known as the total surface area of a cylinder. The total surface area is calculated using the formula:
Total Surface Area = 2πr(h + r) square units
Where r is the radius of the base of the cylinder and h is the height of the cylinder.
Volume of Cylinders
The volume of a cylinder shows how much space is inside it. It tells us how much it can hold.
The volume of a cylinder can be found by using the formula: Volume = πr²h cubic units
Confusion between Surface Area and Volume
Students sometimes confuse the formulas and calculations for surface area and volume. Remember that surface area measures the outer surface, while volume measures the space inside.
Mistake 1
Using the Wrong Formula for the Shape
Each shape has its own formula for surface area. Ensure you are using the correct formula for prisms or cylinders, as they differ significantly.
Mistake 2
Incorrectly Calculating Cylinder Surface Area
A common mistake is forgetting to include both the curved surface and the bases in the total surface area of a cylinder. Always include both parts: Total Surface Area = Curved Surface Area + Base Areas.
Mistake 3
Misunderstanding Dimensions
Students often confuse height and radius or height and width. Ensure you understand the dimensions required in the formula for accurate calculations.
Mistake 4
Using the Wrong Value for π
A common mistake is using 22 as the value of π. Instead, use accurate values like 22/7 or 3.14. π is crucial for calculations involving circles, so always use the correct value.
Mistake 5
Solved Examples of Surface Area of Prisms and Cylinders
Find the surface area of a rectangular prism with a length of 8 cm, a width of 5 cm, and a height of 10 cm.
Surface Area = 340 cm²
Problem 1
Given l = 8 cm, w = 5 cm, h = 10 cm. Use the formula: Surface Area = 2lw + 2lh + 2wh = 2(8)(5) + 2(8)(10) + 2(5)(10) = 80 + 160 + 100 = 340 cm²
Find the total surface area of a cylinder with a radius of 4 cm and a height of 9 cm.
Explanation
Total Surface Area = 326.56 cm²
Problem 2
Use the formula: Total Surface Area = 2πr(h + r) = 2 × 3.14 × 4 × (9 + 4) = 2 × 3.14 × 4 × 13 = 326.56 cm²
A cylinder has a radius of 5 cm and a height of 12 cm. Find the total surface area.
Explanation
Total Surface Area = 534.6 cm²
Problem 3
Use the formula: Total Surface Area = 2πr(h + r) = 2 × 3.14 × 5 × (12 + 5) = 2 × 3.14 × 5 × 17 = 534.6 cm²
Find the surface area of a triangular prism with a base perimeter of 24 cm, a base area of 30 cm², and a height of 10 cm.
Explanation
Surface Area = 480 cm²
Problem 4
Surface Area = (Base Perimeter × Height) + 2 × Base Area = (24 × 10) + 2 × 30 = 240 + 60 = 480 cm²
The radius of a cylinder is 7 cm, and its total surface area is 660 cm². Find the height.
Explanation
Height = 10 cm
It is the total area that covers the outside of the shape, including its faces or curved surface and bases.
1.What are the two types of surface area in a cylinder?
2.What is the difference between height and slant height in prisms and cylinders?
3.What is the unit for measuring surface area?
4.How do you calculate the surface area of a rectangular prism?
Common Mistakes and How to Avoid Them in the Surface Area of Prisms and Cylinders
Students often make mistakes while calculating the surface area of prisms and cylinders, leading to incorrect answers. Below are some common mistakes and 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
