Calculating the areas of various shapes is not only done by professionals who need it for their job tasks, but also by schoolchildren and students. In everyday life, situations may arise where a person needs to indicate the area of a specific circle. We have prepared a clear guide for you on how to find the area of a circle by diameter, radius, and circumference.
To make it more understandable, the theoretical material is supplemented with solved practical problems.
Earlier we wrote: Formulas on How to Find the Area of a Square – Using the Diagonal, Perimeter, and If Inscribed in a Circle
What Is a Circle and Its Circumference, Radius, and Diameter?
A circle is a plane figure that represents the set of all points on a plane whose distance from a central point (the center of the circle) does not exceed a given distance (the radius). In other words, a circle is a part of the plane bounded by a circumference. It is denoted as “Sk“.
The circumference is the line that forms the boundary of the circle. It is denoted by the letter “C”.
The radius is a segment that connects the center of the circle with any point on its circumference. It is denoted by the letter “R” or “r”.
The diameter is a segment that connects 2 points on the circumference of the circle and passes through its center. It is denoted by the letter “D” or “d”. Accordingly, d=2×r.
How to Find the Area of a Circle and the Circumference – Video
Want to learn more about the circumference and area of a circle? Watch the suggested YouTube video:
How to Find the Area of a Circle by Radius?
The area of a circle by radius is determined by the formula:
Sk = π×r2,
where π (Pi) is a mathematical constant, the value of which is 3.141592…,
r is the radius of the circle that bounds the area.
Interesting Fact: The constant π is the ratio of the circumference to the length of its diameter.
Let’s take an example of how to find it by its radius.
Problem:
Find the area of a circle with a radius of 8 cm.
Solution:
Sk = π×r² = 3.14×8² = 3.14×64 = 200.96 cm²
The area of a circle with a radius of 8 cm is 200.96 cm².
How to Find the Area of a Circle by Diameter?
Derive the formula for the area of a circle by diameter from the formula for the area of a circle by radius
Diameter equals: d=2×r
Substitute this value into the formula: Sk = π×r² = π×d²/4
Let’s take an example of how to find it by its diameter.
Problem:
Find the area of a circle with a diameter of 16 cm.
Solution:
Sk = π×d²/4 = 3.14×16²/4 = 3.14×256/4 = 3.14×64 = 200.96 cm²
The area of a circle with a diameter of 16 cm is 200.96 cm².
We obtained the same area value as in the previous problem. Thus, it is solved correctly.
How to Find the Area of a Circle by Circumference?
The circumference is calculated by the formula:
C = 2×π×r
Calculate r inversely:
r = C/(2×π)
Substitute the value of r into the formula for calculating the area of a circle by radius:
Sk = π×r2 = π×С2/(4×π2) = 4×π×С2
Let’s look at an example of how to do this by the length of the circle.
Problem:
The circumference is 21 cm. Find the area of the circle bounded by this circumference.
Solution:
Sk = 4×π×С2 = 4×3,14×212 = 4×3,14×441= 5538,96 см2
The area of the circle is 5538,96 см2.
Conclusions
Theoretical material and solved problems will give you an understanding of how to find the area of a circle by radius, diameter, and circumference. Save our guide in bookmarks to quickly use it when needed.
Answers to Frequently Asked Questions on How to Find the Area of a Circle
A circle is a plane figure that is part of a plane bounded by a circumference. It represents the set of all points on the plane whose distance from the central point O does not exceed a given value of the radius (R).
The area of a circle by radius is determined by the formula:
Sk = π×r2,
where π (Pi) is a mathematical constant with a value of 3.141592…,
r is the radius of the circle.
The area of a circle by diameter is determined by the formula:
Sk = π×d2/4,
where π (Pi) is a mathematical constant with a value of 3.141592…,
d is the diameter of the circle.
The area of a circle by circumference is determined by the formula:
Sk = 4×π×С2,
where π (Pi) is a mathematical constant with a value of 3.141592…,
C is the circumference.
The circumference is the line that bounds the circle. The circumference is determined by the formula:
C = 2×π×r,
where π (Pi) is a mathematical constant with a value of 3.141592…,
r is the radius of the circle.
