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102 LearnersLast updated on October 28, 2025
Base Area of a Circle
The base area of a circle refers to the area of the flat, circular surface, which is a 2-dimensional surface. A circle is a simple closed shape formed by the set of all points in a plane that are at a given distance from a given point, the center.
What is the Base Area of a Circle?
The base area of a circle is simply the area of the circular surface. The formula to calculate the base area of a circle is πr², where r is the radius of the circle.
What is the Base Area of a Circle Formula?
The formula for the base area of a circle is πr². In this formula, π (pi) is approximately equal to 3.1416, and r is the radius of the circle.
How to Find the Base Area of a Circle?
To find the base area of a circle, use the formula πr². Follow these steps:
Step 1: Determine the radius of the circle and denote it as r.
Step 2: If the radius is given, find the base area of the circle using the formula πr². If the diameter is given instead of the radius, use the formula (π/4)D², where D is the diameter.
Step 3: Write the answer with square units.
For example, if the radius of a circle is 5 cm, find the base area: Base area = πr² = π × 5² = 3.1416 × 25 = 78.54 cm²
Tips and Tricks for the Base Area of a Circle
Here are some tips and tricks to help solve the problem easily:
- Remember, the base is a circle.
- Square the radius first.
- Use the correct π value.
- Check the units.
- Don’t confuse with circumference.
Common Mistakes and How to Avoid Them on the Base Area of a Circle
When finding the base area of a circle, small mistakes can lead to the wrong answer. Here are some common mistakes that can be avoided.
Mistake 1
Confusing radius with diameter
Students often mistakenly use the diameter directly in the formula instead of the radius. Always check whether the given measurement is the radius or the diameter before substituting it.
Mistake 2
Using the wrong formula
Some students mix up the base area with the circumference or volume formula. The base area of a circle is calculated using the formula πr².
Mistake 3
Forgetting to square the radius
First, square the radius (r²), then multiply the result by π to find the base area.
Mistake 4
Using the wrong value of π
Sometimes students use an incorrect value for π. Use π = 3.1416 for decimals and π = 22/7 when working with fractions.
Mistake 5
Mistaking circumference for area
Students may use the formula 2πr (circumference) instead of πr² for the base area. Always check whether the question is asking for the base area or the circumference.
Solved Examples for Base Area of a Circle
Problem 1
The radius of a circular garden is 3 m. Find the base area.
28.26 m²
Explanation
To find the base area of the circle, use the formula πr².
The value of π is 3.14. Radius is r = 3.
πr² = 3.14 × 3² = 3.14 × 9 = 28.26 m²
Problem 2
Radius = 4.5 m. Find the base area of the circular park.
63.62 m²
Explanation
To find the base area of the circular park, use the formula πr².
Radius = 4.5.
The value of π is 3.1416.
The base area = πr² = 3.1416 × 4.5² = 3.1416 × 20.25 = 63.6174 ≈ 63.62 m²
Problem 3
A circular swimming pool has a diameter of 8 m. Find the base area.
50.24 m²
Explanation
The diameter of the pool is 8 m.
Radius = Diameter ÷ 2
Radius of the pool = 8 ÷ 2 = 4 m
Then find the base area of the circle = πr² r² = 4² = 16
The base area = 3.14 × 16 = 50.24
The base area = 50.24 m²
Problem 4
The base area is 50.24 m². Find the radius.
r = 4 m
Explanation
To find the radius A = πr²
50.24 = 3.14 × r²
r² = 50.24 / 3.14
r² = 16
Take the square root of both sides r = √16
r = 4 m
Problem 5
A circular tabletop has a base radius of 7.8 cm. Find the base area to determine the cover size.
191.3 cm²
Explanation
The formula for the base area of a circle = πr²
r = 7.8
π = 3.14
Base area = πr² = 3.14 × (7.8)² = 3.14 × 60.84 = 191.3 cm²
FAQs on Base Area of a Circle
1.What is the base area of a circle?
2.What is the formula for the base area of a circle?
3.What is the formula for the base area of a circle with a diameter?
4.Is the base area the same as the circumference of a circle?
5.What unit is used for the base area of a circle?
Important Glossary for Base Area of a Circle
- Base Area: The area of the flat circular surface, calculated using the formula πr².
- Circle: A 2-dimensional shape defined by all points equidistant from a center point.
- Radius: The distance from the center of the circle to any point on its edge.
- Diameter: The distance across the circle, passing through its center; equal to twice the radius (d = 2r).
- Pi (π): A mathematical constant approximately equal to 3.1416, used in calculations involving circles.
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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
