About Area and circumference of a circle formula
Let's begin our exploration of circle formulas by revisiting the fundamental concept of a circle. A circle can be defined as a collection of points in a plane that are equidistant from a fixed point, known as the centre of a circle. The distance from the centre to any point on the circle's boundary is referred to as the radius.In this mathematics article, we'll explore the circle formulas. We'll also go through some examples to understand it better.What are all Circle Formulas?The circle formula is often expressed in terms of its circumference (\(C\)) and area (\(A\)). The circumference is the distance around the circle, while the area is the measure of the region enclosed by the circle. The circle formula reveals the relationship between the radius (\(r\)) and these two fundamental properties of a circle.Circle FormulasCircle formulas provide a means to calculate various parameters such as area, circumference, and radius of a circle. Different formulas are available for different parameters, which can be expressed as follows:Where: \(r\) represents the radius, and \(\pi\) is the mathematical constant pi.Other Circle FormulasHere are some other formulas related to circles: Description Formulas Chord Length of a Circle \(L = 2r \sin\left(\frac{\theta}{2}\right)\) Arc Length of a Circle \(L = 2 \pi r \left(\frac{\theta}{360^{\circ}}\right)\) Sector Area of a Circle \(A = \pi r^{2} \left(\frac{\theta}{360^{\circ}}\right)\) Where: \(r\) is the radius of the circle, \(\theta\) is the central angle (in degrees), and \(\pi\) is the mathematical constant pi.Now, let's delve into a few examples to better understand the formulas of the circle.Circle Formula Solved ExamplesExample 1. Find the area of a circle with a radius of \(5\) units.Solution.Given: Radius \((r) = 5\) units Using the area of a circle formula: \(A = \pi r^{2}\)Substituting the value of the radius: \(A = \pi (5)^{2}\)Calculating the area: \(A = 25\pi\) square units Answer: The area of the circle is \(25\pi\) square units.Example 2. Find the circumference of a circle with a radius of \(5\) cm.Solution.Given: Radius \((r) = 5\) cm Using the circumference formula \(C = 2\pi r\), where \(\pi \approx 3.14159\): \(C = 2 \times 3.14159 \times 5\) \(\Rightarrow\) \(C \approx 31.4159\) cmAnswer: The circumference of the circle is approximately \(31.4159\) cm.Example 3. The area of a circular swimming pool is \(154\) square meters. Find its radius.Solution.Given: Area \((A) = 154\) square meters Using the area of a circle formula: \(A = \pi r^{2}\)Substituting the value of the area:
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The diameter of the circle. Half the diameter is the radius. Square the radius and multiply by pi to find the area of the circle. Question How do I calculate the circumference of a circle? To find the circumference of a circle, simply multiply the diameter by pi (3.14). For example: If d= 23cm, C= 3.14 x 23cm, so C= 72.22cm. Question Is this formula correct? C = pi * d calculates the circumference (distance around the outside of the circle). D in the formula refers to the diameter which is the width of the circle. The formula for the area of a circle is A = pi * r * r where r is the radius (diameter / 2). See more answers Ask a Question 200 characters left Include your email address to get a message when this question is answered. Submit Advertisement Thanks for submitting a tip for review! References About This Article Article SummaryXYou can find the area of a circle using the radius, the diameter, or the circumference. To find the area using the radius, or the length from the center of the circle to the edge, use the formula area = πr^2, where r is the radius. For example, if the radius of the circle is 6 inches, first you would square 6 and get 36. Then, you would multiply 36 by π and get 113.04. Therefore, the area of the circle is 113.04 inches squared. To find the area using the diameter, or the
