105 LearnersLast updated on August 5th, 2025
Surface Area of Disc
A disc is a 2-dimensional shape with a circular boundary. The surface area of the disc is the total area covered by its circular surface. In this article, we will learn about the surface area of a disc.
What is the Surface Area of a Disc?
The surface area of a disc is the total area occupied by the surface of the disc. It is measured in square units.
A disc is a flat, circular shape that can be visualized as a circle lying flat on a plane. Unlike a cone, a disc does not have a height or a curved side. The surface area of a disc is simply the area of the circle that forms its boundary.
Surface Area of a Disc Formula
A disc has only one type of surface area, which is the area of the circle forming the disc. The formula to calculate the surface area of a disc is given by: Surface Area = πr² square units Here, r is the radius of the disc.
Calculation of Surface Area of a Disc
The surface area of a disc is the area of the circular region enclosed by its boundary. The formula for the surface area of a disc is:
Surface Area = πr² Where r is the radius of the disc. This formula is derived from the formula for the area of a circle.
Examples of Surface Area of a Disc
Let's consider some examples to understand how to calculate the surface area of a disc. If you have a disc with a known radius, you can plug it into the formula to find the surface area.
Volume of a Disc
A disc is a 2-dimensional shape, so it does not have a volume. Volume is a measure of space occupied by a 3-dimensional object, whereas a disc only has area.
Confusion between Area and Circumference
Students sometimes confuse the formula for the area of a disc (πr²) with the formula for the circumference of a circle (2πr). Remember that the surface area of a disc is about the space inside, not the length around it.
Mistake 1
Using Diameter Instead of Radius
Some students mistakenly use the diameter instead of the radius in the formula for the surface area of a disc. Always remember that the formula requires the radius, which is half the diameter.
Mistake 2
Using the Wrong Value for π
A common mistake is using incorrect values for π, like 22 instead of 22/7 or 3.14. Use accurate values for π to get correct results.
Mistake 3
Forgetting Units
It is essential to include units in your final answer. Surface area is measured in square units, like cm², m², or in².
Mistake 4
Assuming a Disc Has Volume
Some students mistakenly try to calculate the volume of a disc. Remember, a disc is a 2-dimensional shape and does not have volume.
Mistake 5
Solved Examples of Surface Area of Disc
Find the surface area of a disc with a radius of 7 cm.
Surface Area = 154 cm²
Problem 1
Given r = 7 cm. Use the formula: Surface Area = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 cm²
Find the surface area of a disc with radius 5 cm.
Explanation
Surface Area = 78.5 cm²
Problem 2
Use the formula: Surface Area = πr² = 3.14 × 5 × 5 = 3.14 × 25 = 78.5 cm²
A disc has a radius of 6 cm. Find the surface area.
Explanation
Surface Area = 113.04 cm²
Problem 3
Use the formula: Surface Area = πr² = 3.14 × 6 × 6 = 3.14 × 36 = 113.04 cm²
Find the surface area of a disc with radius 3.5 cm.
Explanation
Surface Area = 38.5 cm²
Problem 4
Surface Area = πr² = (22/7) × 3.5 × 3.5 = 22 × 0.5 × 3.5 = 11 × 3.5 = 38.5 cm²
The surface area of a disc is 660 cm². Find the radius.
Explanation
Radius = 14.5 cm
It is the total area that covers the surface of the disc, calculated using the formula πr².
1.Does a disc have a volume?
2.What is the formula for calculating the surface area of a disc?
3.Is surface area measured in square units?
4.Can the surface area of a disc be negative?
Common Mistakes and How to Avoid Them in the Surface Area of a Disc
Students often make mistakes while calculating the surface area of a disc, which leads to wrong 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.
Fun Fact
: She has songs for each table which helps her to remember the tables
