Area of Disc
2026-02-28 13:15 Diff
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Last updated on September 17, 2025

Area is the space inside the boundaries of a two-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of the disc.

What is the Area of Disc?

A disc is a circular two-dimensional shape where every point on the boundary is equidistant from the center. The area of the disc is the total space it encloses within its boundary.

The defining characteristic of a disc is its radius, which is the distance from the center to any point on the boundary.

Area of the Disc Formula

To find the area of the disc, we use the formula: πr², where r is the radius of the disc. This formula is derived from the geometric properties of a circle, where π (pi) is a constant approximately equal to 3.14159.

Derivation of the formula: The formula for the area of the disc is derived from integrating the infinitesimal circular rings that make up the disc. Each ring has an infinitesimal width dr and a circumference 2πr. Integrating these rings from the center (r=0) to the boundary (r=R) gives: Area = ∫ (2πr dr) from 0 to R = πr² Therefore, the area of the disc = πr²

How to Find the Area of Disc?

We can find the area of the disc using a straightforward method by applying the formula with the given radius. Here’s how: Method Using the Radius If the radius r is given, we find the area of the disc using the formula Area = πr²

For example, if the radius of a disc is 7 cm, what will be the area of the disc? Area = π × 7² = π × 49 ≈ 153.94 cm² The area of the disc is approximately 153.94 cm²

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Unit of Area of Disc

We measure the area of a disc in square units. The measurement depends on the system used:

In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²).

In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).

Special Cases or Variations for the Area of Disc

Since a disc is a circular shape, its area is calculated using its radius. However, there are variations depending on the given data:

Case 1: Given the Diameter If the diameter is given, the radius r is half the diameter, and the area is found using Area = πr².

Case 2: Given the Circumference If the circumference is given as C, the radius can be found using r = C/(2π) and then the area using Area = πr².

Tips and Tricks for Area of Disc

To ensure accurate results while calculating the area of the disc, consider these tips and tricks:

  • Always verify the radius; if the diameter is given, divide it by 2 to get the radius.
     
  • Use the value of π according to the precision required: 3.14 for rough estimates or 3.14159 for more precision.
     
  • Ensure all measurements are in the same units when calculating area.

Common Mistakes and How to Avoid Them in Area of Disc

It is common for kids to make mistakes while finding the area of the disc. Let’s take a look at some mistakes made by kids.

Problem 1

A pizza has a radius of 15 cm. What will be the area?

Okay, lets begin

We will find the area as approximately 706.86 cm².

Explanation

Here, the radius r is 15 cm.

The area of the disc = πr² = π × 15² = π × 225 ≈ 706.86 cm².

Well explained 👍

Problem 2

What will be the area of a circular garden if the diameter is given as 10 m?

Okay, lets begin

We will find the area as approximately 78.54 m².

Explanation

If the diameter is given, the radius r = diameter/2 = 10/2 = 5 m.

The area will be π × 5² ≈ 78.54 m².

Well explained 👍

Problem 3

The area of a circular field is 314 m². Find the length of the radius.

Okay, lets begin

We find the radius as approximately 10 m.

Explanation

To find the radius, use the formula area = πr².

Given area = 314 m², solve 314 = πr² for r: 314/π = r² r ≈ √(314/π) ≈ 10 m.

Well explained 👍

Problem 4

Find the area of a circular lake if its circumference is 31.4 m.

Okay, lets begin

We will find the area as approximately 78.54 m².

Explanation

The circumference C = 2πr.

Given C = 31.4 m, we find the radius: r = 31.4/(2π) ≈ 5 m.

Area = πr² = π × 5² ≈ 78.54 m².

Well explained 👍

Problem 5

Help Lisa calculate the area of a circular table top if the radius is 0.6 m.

Okay, lets begin

We will find the area as approximately 1.13 m².

Explanation

The radius is 0.6 m.

Thus, the area = π × 0.6² ≈ 1.13 m².

Well explained 👍

FAQs on Area of Disc

1.Is it possible for the area of the disc to be negative?

No, the area of the disc can never be negative. The area of any shape will always be positive.

2.How to find the area of a disc if the diameter is given?

If the diameter is given, find the radius by dividing it by 2, and then use the formula Area = πr².

3.How to find the area of a disc if only the circumference is given?

If the circumference is given, find the radius using r = C/(2π) and then use the formula Area = πr².

4.How is the circumference of the disc calculated?

The circumference of the disc is calculated using the formula C = 2πr, where r is the radius.

5.What is meant by the area of the disc?

The area of the disc is the total space occupied by the disc.

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