How to find the Area of a Circle: Definition, Formula, Worksheets

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How to find the Area of a Circle (using Formula for Area of a Circle)

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Key Points about Area of a Circle

The area of a circle is the amount of space enclosed within the circumference of a circle.
The formula for calculating the area of a circle is πr² or π(d/2)².
Understanding the area of a circle is important in many fields, including mathematics, engineering, and physics.

What is the Area of a Circle Equation?

The area of a circle is a fundamental concept in geometry that measures the size of a circle’s surface. It is the amount of space enclosed within the circumference of a circle. The area of a circle can be calculated using the circle’s radius or diameter.

The formula for calculating the area of a circle is πr², where r is the radius of the circle. The value of π is approximately 3.14, and the radius is the distance from the center of the circle to any point on its circumference. The diameter of a circle is twice the length of its radius, so the formula for calculating the area of a circle using the diameter is π(d/2)², where d is the diameter of the circle.

Understanding the area of a circle is important in many fields, including mathematics, engineering, and physics. It is used to calculate the surface area of circular objects, such as wheels, plates, and pipes. It is also used in trigonometry to calculate the area of sectors and in calculus to calculate volumes of revolution.

The Area of a Circle is all of the area that is inside of a circle. The Area of a Circle Formula states that Area is equal to pi time the radius squared. Usually you find the area of a circle using radius but sometimes you will have to find the Area of a Circle with diameter. The diameter is twice as long as the radius, or the radius is half of the diameter. The formula for how to find Area of a Circle is area equals pi times the radius squared. If you have the area of a circle with diameter that means that you have to divide the diameter by two to get the radius. Once you have the radius you can use the Area of a Circle formula. When simplifying you need to do follow the order of operations. You must square the radius and then multiply it times pi.

Common Core Standard: 7.G.5
Related Topics: Area of a Semicircle, Circumference of a Circle, Perimeter of a Semicircle, Complementary Angles, Supplementary Angles, Vertical Angles
Return To: Home, 7th Grade

How to find Area of a Circle

Area of a Circle Definition

The area of a circle is defined as the amount of space enclosed within the boundary of a circle in a two-dimensional plane. It is measured in square units such as m², cm², etc. The area of a circle is denoted by the letter A.

The formula to calculate the area of a circle is A = πr², where r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14. Alternatively, the area of a circle can also be calculated using the diameter of the circle with the formula A = π(d/2)², where d is the diameter of the circle.

The value of π is a constant term used in the formula of the area of a circle. It is an irrational number, which means that its decimal representation never ends or repeats. The value of π is approximately 3.14159265359, but it is often rounded to 3.14 for practical purposes.

Understanding the concept of the area of a circle is essential in many fields such as mathematics, physics, engineering, and architecture. It is used to calculate the area of circular objects such as wheels, plates, and coins. Additionally, the area of a circle is also used in the calculation of the circumference, diameter, and radius of a circle.

Area of a Circle Formula

Calculating the area of a circle is an essential skill in mathematics. The formula for the area of a circle is simple and easy to use. It is given by:

A = πr²

Where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Using the Area of a Circle Formula

To use the area of a circle formula, you need to know the radius of the circle. If you don’t know the radius but know the diameter, you can easily find the radius by dividing the diameter by 2. Once you have the radius, plug it into the formula, and you can calculate the area of the circle.

For example, suppose you have a circle with a radius of 5 cm. Using the formula, you can calculate the area of the circle as follows:

A = πr²
A = π(5)²
A = 25π

So, the area of the circle is 25π square cm.

Area of a Circle Calculator

Calculating the area of a circle can be time-consuming, especially when dealing with large circles. To make things easier, you can use an area of a circle calculator. There are many online calculators available that can quickly calculate the area of a circle for you. These calculators typically require you to input the radius or diameter of the circle, and they will do the rest of the calculations for you.

Using an area of a circle calculator can be especially useful when you need to make quick calculations or estimates. However, it’s important to remember that these calculators only provide approximations and should not be relied upon for precise calculations.

In conclusion, the area of a circle formula is a simple and easy-to-use formula that can be used to calculate the area of a circle. By knowing the radius of the circle, you can plug it into the formula and calculate the area. If you need to make quick calculations or estimates, you can use an area of a circle calculator, but always keep in mind that these calculators only provide approximations.

5 Easy Steps for solving Area of a Circle Examples

Calculating the area of a circle is a fundamental concept in geometry. Here are a few examples to help understand the formula and its practical applications.

Use the Area of a Circle Formula: Area equals pi time the radius squared.
The first step is to square the radius.
Then you multiply the square of the radius times pi. (3.14)
After you do that make sure you check your units and ensure that they are correct.
If the circle gives you the diameter then you should divide it by two first.

Example 1

Suppose a circle has a radius of 5 cm. To find its area, we use the formula:

A = πr²

where A is the area and r is the radius. Substituting the given value of r into the formula, we get:

A = π(5)²
A = 25π

Hence, the area of the circle is approximately 78.54 cm².

Example 2

Suppose a circular pizza has a diameter of 16 inches. To find the area of the pizza, we first need to find the radius. Since the diameter is the distance across the circle, we can use the formula:

d = 2r

where d is the diameter and r is the radius. Substituting the given value of d into the formula, we get:

16 = 2r
r = 8

Now that we know the radius is 8 inches, we can use the formula for area:

A = πr²
A = π(8)²
A = 64π

Hence, the area of the pizza is approximately 201.06 inches².

Example 3

Suppose a circular garden has a circumference of 50 ft. To find the area of the garden, we first need to find the radius. Since the circumference is the distance around the circle, we can use the formula:

C = 2πr

where C is the circumference and r is the radius. Substituting the given value of C into the formula, we get:

50 = 2πr
r = 25/π

Now that we know the radius is 7.96 ft, we can use the formula for area:

A = πr²
A = π(7.96)²
A = 199.04π

Hence, the area of the garden is approximately 625.01 ft².

These examples demonstrate how the formula for the area of a circle can be used in various real-world scenarios.

5 Quick Area of a Circle Practice Problems

How to Find the Area of a Circle with Radius

Calculating the area of a circle with radius is a simple process that involves using the formula A = πr², where A is the area and r is the radius. In order to find the area of a circle with radius, you need to follow these steps:

Measure the radius of the circle: The radius is the distance from the center of the circle to its edge. Use a ruler or a measuring tape to measure the length of the radius.
Square the radius: Once you have the length of the radius, square it by multiplying it by itself. This will give you the value of r².
Multiply the squared radius by π: After you have the value of r², multiply it by π (pi), which is approximately equal to 3.14. The resulting value is the area of the circle.

It is important to note that the units of measurement for the radius and the area must be the same. For example, if the radius is measured in inches, the area will be in square inches.

Here is an example calculation of the area of a circle with radius:

Suppose the radius of a circle is 5 cm. To find its area, we need to square the radius (5 x 5 = 25) and multiply it by π (25 x 3.14 = 78.5). Therefore, the area of the circle is 78.5 square centimeters.

In conclusion, finding the area of a circle with radius is a straightforward process that involves squaring the radius and multiplying it by π. By following the steps outlined above, anyone can calculate the area of a circle with radius with ease.

How to Find the Area of a Circle with Diameter

To find the area of a circle with diameter, you can use the formula: Area of a circle = π × (d/2)², where d is the diameter of the circle and π is approximately equal to 3.14.

Here are the steps to find the area of a circle with diameter:

Measure the diameter of the circle: Use a ruler or tape measure to measure the diameter of the circle. The diameter is the distance across the circle, passing through the center point.
Divide the diameter by 2: Since the formula for the area of a circle uses the radius, which is half the diameter, divide the diameter by 2 to get the radius.
Square the radius: Once you have the radius, square it by multiplying it by itself.
Multiply by π: Finally, multiply the squared radius by π (approximately 3.14) to get the area of the circle.

It’s important to note that the units for the diameter, radius, and area should all be the same. For example, if the diameter is measured in inches, the radius and area should also be in inches.

Using this formula, you can easily find the area of a circle with diameter, whether you’re working on a math problem or need to calculate the area of a circular object in real life.

How to find the Area of a Circle with Circumference

To find the area of a circle with its circumference, one can use the formula A = (C^2)/(4π), where A is the area, C is the circumference, and π is the mathematical constant pi (approximately equal to 3.14).

First, measure the circumference of the circle using a measuring tape or a ruler. Then, plug this value into the formula and solve for A.

For example, if the circumference of a circle is 20 cm, the area can be calculated as follows:

A = (20^2)/(4π) A = 100/π A ≈ 31.83 cm^2

Therefore, the area of the circle is approximately 31.83 square centimeters.

It is important to note that this formula only works if the circumference is known. If the radius or diameter is known instead, a different formula should be used. One can also use online calculators such as the Circumference and Area of a Circle Calculator to find the area of a circle with its circumference.

FAQ about Area of a Circle

What is the formula for finding the area of a circle?

The formula for finding the area of a circle is A = πr^2, where A is the area of the circle, r is the radius of the circle, and π is a constant value approximately equal to 3.14.

What is the relationship between the radius and area of a circle?

The area of a circle is directly proportional to the square of its radius. This means that if the radius of a circle is doubled, its area will be four times greater.

How do you calculate the area of a circle with a given diameter?

To calculate the area of a circle with a given diameter, divide the diameter by 2 to find the radius, and then use the formula A = πr^2 to find the area.

What is the significance of the constant pi in the formula for the area of a circle?

The constant π is significant in the formula for the area of a circle because it represents the ratio of the circumference of a circle to its diameter. This ratio is the same for all circles, regardless of their size.

How can the area of a circle be used in real-world applications?

The area of a circle can be used in real-world applications such as calculating the amount of material needed to cover a circular surface, such as a pizza or a circular table top.

What are some common misconceptions about the area of a circle?

One common misconception about the area of a circle is that it is equal to the circumference of the circle. Another misconception is that the diameter of a circle is equal to its radius.

How to figure the area of a circle?

To figure out the area of a circle, simply square the radius and multiply by pi. The formula is A = πr^2.

What are the 2 formulas for area of a circle?

There is only one formula for the area of a circle, which is A = πr^2. However, there is another formula that can be used to find the radius of a circle, which is r = √(A/π).

What is 2 pi r squared used for?

The formula 2πr is used to calculate the circumference of a circle, while the formula πr^2 is used to calculate the area of a circle.

Area of a Circle Worksheet Video Explanation

Watch our free video on How to find Area of a Circle. This video shows how to solve problems that are on our free finding the Area of a Circle worksheet that you can get by submitting your email above.

Watch the free How to find Area of a Circle video on YouTube here: Area of a Circle Video

Video Transcript:

This video is about how to find the area of a circle. You can get the 7th grade area of a circle worksheet used in this video for free by clicking on the link in the description below.

Finding area of circle of a circle you have to use the area of a circle formula. This circle area formula says that the area of a circle is equal to pi times the radius squared. The radius is from the middle point of the circle to the outer edge. It does not matter which way you draw the radius because the distance from the center of the circle to the outer edge will be equal no matter where you draw it.

Now let’s say you’re told that the radius is 4 inches. You will take this information and you will substitute it into the formula where radius is supposed to go. So your formula will change from pi r squared into pi times the radius, which in this case is 4, squared and then you simplify 4 times 4. 4 squared which is 16 and then you do pi times 16, which is equal to 50.27 inches squared.

You may also be given a problem in which instead of giving you the radius they give you the whole diameter of the circle. Now the diameter of the circle is the distance all the way across the middle of the circle. Instead of just being from the middle to the outside edge, it’s from one edge of the circle directly across to the other edge of the circle that goes through the middle.

In this case you have to remember that the diameter is equal to twice the size of the radius. In other words, you have to take the diameter and divide it by 2 in order to get the radius. If they gave you a diameter of let’s say 12 feet you have to take the diameter, in this case is 12 feet, and divide it by 2 in order to get the radius. So if the diameter was 12 feet then the radius would be equal to 6 feet. Once you know the radius, in this case is 6, then you can use your formula which is area is equal to pi times the radius squared.

Again we know the radius is 6 this time, so we take 6 substitute it in for r so you do pi times 6 squared. Then you do 6 squared first, according to the order of operations, which is 36 and then you do pi times 36 which is 113.1 feet squared.

Let’s try a couple practice problems on our area of a circle worksheet. Problem number one to practice how to find area of circle gives us 5 inches for the radius. Now we know the circle formula area equals pi times the radius squared.

In this case we know the radius is 5 inches and I know it’s referring to the radius because it’s only half of the circle. If it went all the way across that would be the diameter, but in this case because it’s only half, that’s going to be the radius. We know the radius is 5 inches so we’re going to say radius equals 5, and now we can substitute 5 in for where the radius used to be.

So we’re going to take our formula which is area equals pi times the radius, which in this case is 5 squared, then order of operations says we do 5 squared so we do pi times 5 squared which is 25. And then we do pi times 25 which gives us 78.55 inches squared and that’s going to be our solution.

Moving on to the fourth problem on our area of a circle worksheet it gives us 22 centimeters for the diameter. So this time we are figuring out area of a circle with diameter. I know its diameter because the line goes all the way across the circle, so because it goes all the way across that’s referring to the diameter.

We know this time that we’re going to be using or we’re going to be starting with the diameter. In this case the diameter is equal to 22 centimeters. Now if you remember diameter is twice the radius which means in order to get the radius you have to take the diameter and divide it by 2. S the diameter, which is 22 divided by 2 is 11, so 22 divided by 2 is 11. We know the radius now is 11 and we can take the radius which is 11 and now we can substitute it in for r in our area formula. We have area equals pi times the radius which in this case is 11 squared.

Then you’re going to square 11 so 11 times 11 is 121 and then you’re going to do pi times 121 and then pi times 121 is 380.13 centimeters squared. If you’re finding area of a circle with diameter you just have the extra step of dividing diameter by two to get the radius.