# How to find the area and circumference of a circle

A circle is the set of all points in a plane that are a fixed distance from a fixed point, called the center, and are separated by a fixed distance, called the radius. A circle's perimeter, or distance around it, is its circumference (C). A circle's area (A) is the amount of space it occupies or the area it encompasses.

Calculate the area of a circle by using the formula:

Step 1. The area of a circle can be determined using two distinct formulas based on the diameter or radius:

A =π or A = π , where is a mathematical constant of about 3.14.’ r‘ is the radius, and ‘d’ seems to be the diameter.

These equations are essentially the same because the radius of a circle is equal to half of its diameter. The area can be measured in feet squared ( ), meters squared ( ), centimeters squared ( ), and other units of length squared.

Step 2. Recognize the various components of the formula. The radius, diameter, and circumference of a circle are the three components needed to calculate its circumference. The radius and diameter are proportional: the radius is half the diameter, and the diameter is double the radius.

A circle's radius (r) is the distance between one point on the circle and its center.

A circle's diameter (d) is the distance between one point on the circle and another exactly opposite it, measured through the center.

The number 3.14159265..., an irrational number with neither a final digit nor a recognized pattern of repeated digits, shows the ratio of circumference divided by diameter.

Step 3.Calculate the circle's radius or diameter. Place one end of a ruler on one side of the circle and the other end on the other side of the circle, passing through the center point. The radius is the distance from the circle's center, while the diameter is the distance from one end to the other.

The radius or diameter is provided radius=4m diameter=6m

Step 4. Solve the problem by putting in the variables. You can put the radius and/or diameter of the circle into the relevant equation once we've determined the radius and/or diameter.

Use A =π  if you know the radius, but A = π  if you know the diameter.

Example: What is the area of a 4 meter radius circle?

By putting the values:

A =π  is a formula that describes the relationship between two variables.

Variables to the plugin: A=π

Radius is squared: The  value is  which equals sixteen.

Multiply by pi (π) if we want to get a more complicated answer

A=π  16 =

Example:

What is the area of a circle with a diameter of 8 meters?

By putting the values

A =π  is a formula that describes the relationship between two variables.

Variables to the plugin: A=π

By multiplying the diameter by two, you can arrive at the following result:2 =8

= 64is the squared result.

Multiply by pi (π) if we want to get a more complicated answer

A=π 64=200.96 meters

Calculate the Area and Circumference of a circle with variables:

Step 1.Calculate the circle's radius or diameter. Some issues will offer you a variable radius or diameter, such as r = (y+ 2) or d = (y+ 4). You can still solve for the area or circumference in this scenario, but your final solution will include that variable. As specified in the problem, write down the radius or diameter.

As an illustration: Determine the circumference of a circle with (y = 2) radius.

Step 2.With the information provided, write the formula.

Regardless of whether you're solving for area or circumference, the essential steps of filling in what you know will remain the same. Make a note of the area or circumference formula, and then put in the variables.

As an illustration: Compute the circumference of a circle with a radius of (y +2) and a diameter of (y + 4).

Write the formula: C =2πr

Fill in the details with the provided data: C=2π(y+2)

Step 4.Solve the problem as if the variable was a number. You can now answer the problem normally, using the variable as if it were a number. To simplify the final answer, you may need to apply the distributive property.

As an illustration: Calculate the circumference of a circle with a radius of y=1

C = 2πr=2π(y +2) = 2πy +2π(2) = 6.28y + 12.56

You can insert the value of "y" in the above equation to obtain a whole number solution.

C = 6.28 (1) + 12.56 =18.84 units

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