Surface Area of Disc
2026-02-28 08:27 Diff
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Last updated on August 5, 2025

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.

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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.

Problem 1

Given r = 7 cm. Use the formula: Surface Area = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 cm²

Okay, lets begin

Find the surface area of a disc with radius 5 cm.

Explanation

Surface Area = 78.5 cm²

Well explained 👍

Problem 2

Use the formula: Surface Area = πr² = 3.14 × 5 × 5 = 3.14 × 25 = 78.5 cm²

Okay, lets begin

A disc has a radius of 6 cm. Find the surface area.

Explanation

Surface Area = 113.04 cm²

Well explained 👍

Problem 3

Use the formula: Surface Area = πr² = 3.14 × 6 × 6 = 3.14 × 36 = 113.04 cm²

Okay, lets begin

Find the surface area of a disc with radius 3.5 cm.

Explanation

Surface Area = 38.5 cm²

Well explained 👍

Problem 4

Surface Area = πr² = (22/7) × 3.5 × 3.5 = 22 × 0.5 × 3.5 = 11 × 3.5 = 38.5 cm²

Okay, lets begin

The surface area of a disc is 660 cm². Find the radius.

Explanation

Radius = 14.5 cm

Well explained 👍

It is the total area that covers the surface of the disc, calculated using the formula πr².

1.Does a disc have a volume?

No, a disc is a 2-dimensional shape and does not have a volume.

2.What is the formula for calculating the surface area of a disc?

The formula for the surface area of a disc is πr², where r is the radius of the disc.

3.Is surface area measured in square units?

Yes, surface area is always measured in square units like cm², m², or in².

4.Can the surface area of a disc be negative?

No, the surface area cannot be negative as it represents a physical space.

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.

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: She has songs for each table which helps her to remember the tables