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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.
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.
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
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
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).
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.
To ensure accurate results while calculating the area of the disc, consider these tips and tricks:
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.
A pizza has a radius of 15 cm. What will be the area?
We will find the area as approximately 706.86 cm².
Here, the radius r is 15 cm.
The area of the disc = πr² = π × 15² = π × 225 ≈ 706.86 cm².
What will be the area of a circular garden if the diameter is given as 10 m?
We will find the area as approximately 78.54 m².
If the diameter is given, the radius r = diameter/2 = 10/2 = 5 m.
The area will be π × 5² ≈ 78.54 m².
The area of a circular field is 314 m². Find the length of the radius.
We find the radius as approximately 10 m.
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.
Find the area of a circular lake if its circumference is 31.4 m.
We will find the area as approximately 78.54 m².
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.
Help Lisa calculate the area of a circular table top if the radius is 0.6 m.
We will find the area as approximately 1.13 m².
The radius is 0.6 m.
Thus, the area = π × 0.6² ≈ 1.13 m².
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.
: She has songs for each table which helps her to remember the tables