Math Antics - Circles, Circumference And Area



How to Find the Circumference and Area of a Circle

Three Parts:

A circle is a two-dimensional line that forms a closed loop, where every point on that loop is an equal distance from the center.The circumference (C) of a circle is its perimeter, or the distance around it.The area (A) of a circle is how much space the circle takes up or the region enclosed by the circle.Both area and perimeter can be calculated with simple formulas using the radius or diameter of the circle and the value of pi.

Steps

Calculating the Circumference

  1. Learn the formula for circumference.There are two formulas that can be used to calculate the circumference of a circle:C = 2πrorC = πd, where π is the mathematical constant approximately equal to 3.14,ris equal to the radius, anddis equal to the diameter.
    • Because the radius of a circle is equal to twice its diameter, these equations are essentially the same.
    • The units for circumference can be any unit for the measure of length: feet, miles, meters, centimeters, etc.
  2. Understand the different parts of the formula.There are three components to finding circumference of a circle: radius, diameter, and π. The radius and diameter are related: the radius is equal to half the diameter, while the diameter is equal to double the radius.
    • The radius (r) of a circle is the distance from one point on the circle to the center of the circle.
    • The diameter (d) of a circle is the distance from one point on the circle to another directly opposite it, going through the circle’s center.
    • The Greek letter pi (π) represents the ratio of the circumference divided by the diameter and is represented by the number 3.14159265…, an irrational number that has neither a final digit nor a recognizable pattern of repeating digits.This number is commonly rounded to 3.14 for basic calculations.
  3. Measure the radius or diameter of the circle.Using a ruler, place one end at one side of the circle and place it through the center point to the other side of the circle. The distance to the center of the circle is the radius, while the distance to the other end of the circle is the diameter.
    • In most textbook math problems, the radius or diameter is given to you.
  4. Plug in the variables and solve.Once you have determined the radius and/or diameter of the circle, you can plug these variables into the appropriate equation. If you have the radius, useC = 2πr, but if you have the diameter, useC = πd.
    • For example: What is the circumference of a circle with a radius of 3 cm?
      • Write the formula: C = 2πr
      • Plug in the variables: C = 2π3
      • Multiply through: C = (2*3*π) = 6π = 18.84 cm
    • For example: What is the circumference of a circle with a diameter of 9 m?
      • Write the formula: C = πd
      • Plug in the variables: C = 9π
      • Multiply through: C = (9*π) = 28.26 m
  5. Practice with a few examples.Now that you’ve learned the formula, it’s time to practice with a few examples. The more problems you solve, the easier it becomes to solve them in the future.
    • Find the circumference of a circle with a diameter of 5 ft.
      • C = πd = 5π = 15.7 ft
    • Find the circumference of a circle with a radius of 10 ft.
      • C = 2πr = C = 2π10 = 2 * 10 * π = 62.8 ft.

Calculating the Area

  1. Learn the formula for area of a circle.The area of a circle can be calculated using the diameter or the radius with two different formulas:A = πr2orA = π(d/2)2,where π is the mathematical constant approximately equal to 3.14,ris equal to the radius, anddis the diameter.
    • Because the radius of a circle is equal to half its diameter, these equations are essentially the same.
    • The units for area can be any unit for the measure of length squared: feet squared (ft2), meters squared (m2), centimeters squared (cm2), etc.
  2. Understand the different parts of the formula.There are three components to finding circumference of a circle: radius, diameter, and π. The radius and diameter are related: the radius is equal to half the diameter, while the diameter is equal to double the radius.
    • The radius (r) of a circle is the distance from one point on the circle to the center of the circle.
    • The diameter (d) of a circle is the distance from one point on the circle to another directly opposite it, going through the circle’s center.
    • The Greek letter pi (π) represents the ratio of the circumference divided by the diameter and is represented by the number 3.14159265…, an irrational number that has neither a final digit nor a recognizable pattern of repeating digits.This number is commonly rounded to 3.14 for basic calculations.
  3. Measure the radius or diameter of the circle.Using a ruler, place one end at one side of the circle and place it through the center point to the other side of the circle. The distance to the center of the circle is the radius, while the distance to the other end of the circle is the diameter.
    • In most textbook math problems, the radius or diameter is given to you.
  4. Plug in the variables and solve.Once you have determined the radius and/or diameter of the circle, you can plug these variables into the appropriate equation. If you have the radius, useA = πr2, but if you have the diameter, useA = π(d/2)2.
    • For example: What is the area of a circle with a radius of 3 m?
      • Write the formula:A = πr2
      • Plug in the variables:A = π32
      • Square the radius:r2= 32= 9
      • Multiply by pi:A= 9π = 28.26 m2
    • For example: What is the area of a circle with a diameter of 4 m?
      • Write the formula:A = π(d/2)2
      • Plug in the variables:A = π(4/2)2
      • Divide the diameter by 2:d/2= 4/2 = 2
      • Square the result: 22= 4
      • Multiply by pi:A= 4π = 12.56 m2
  5. Practice with a few examples.Now that you’ve learned the formula, it’s time to practice with a few examples. The more problems you solve, the easier it becomes to solve them in the future.
    • Find the area of a circle with a diameter of 7 ft.
      • A = π(d/2)2= π(7/2)2= π(3.5)2= 12.25 * π= 38.47 ft2.
    • Find the area of a circle with a radius of 3 ft.
      • A = πr2= π32= 9 * π = 28.26 ft2

Calculating Area and Circumference with Variables

  1. Determine the radius or diameter of the circle.Some problems may give you a radius or diameter that has a variable in it: r = (x + 7) or d = (x + 3). In this case, you can still solve for the area or circumference, but your final answer will also have that variable in it. Write down the radius or diameter as it is stated in the problem.
    • For example: Calculate the circumference of a circle with a radius of (x = 1).
  2. Write the formula with the information given.Whether you are solving for area or circumference, you will still follow the basic steps of plugging in what you know. Write down the formula for area or circumference and then write in the variables given.
    • For example: Calculate the circumference of a circle with a radius of (x + 1).
    • Write the formula: C = 2πr
    • Plug in the given information: C = 2π(x+1)
  3. Solve as if the variable were a number.At this point, you can just solve the problem as you normally would, treating the variable as if it were just another number. You may need to use the distributive property to simplify the final answer.
    • For example: Calculate the circumference of a circle with a radius of (x = 1).
    • C = 2πr = 2π(x+1) = 2πx + 2π1 = 2πx +2π = 6.28x + 6.28
    • If you are given the value of “x” later in the problem, you can plug it in and get a whole number answer.
  4. Practice with a few examples.Now that you’ve learned the formula, it’s time to practice with a few examples. The more problems you solve, the easier it becomes to solve them in the future.
    • Find the area of a circle with a radius of 2x.
      • A = πr2= π(2x)2= π4x2= 12.56x2
    • Find the area of a circle with a diameter of (x + 2).
      • A = π(d/2)2= π((x +2)/2)2= ((x +2)2/4)π

Community Q&A

Search
  • Question
    How do we figure circumference if the area of a circle is 3.14 cm squared?
    Top Answerer
    Divide the area by pi; that gives you r ². Find the square root; that gives you r. Double it; that gives you the diameter. Multiply by pi; that gives you the circumference.
    Thanks!
  • Question
    How do I find the area of a circle when I have the circumference?
    wikiHow Contributor
    Community Answer
    Pi x diameter = Pi x (2 x radius) = Circumference So: Radius = Circumference/(2xPi) Once you have the radius, use this formula: Area = Pi x radius^2
    Thanks!
  • Question
    If the radius of a circle is 15.3 centimeters, then what is the diameter?
    Top Answerer
    The diameter is twice the radius.
    Thanks!
  • Question
    How do I find the circumference of a circle within a square with only the measurement of the square length?
    Shamitha Kuppala
    Community Answer
    If the circle is touching the sides of the square, that means that the diameter of the circle equals the length of the square side. Just multiply the diameter by pi, and you have your circumference!
    Thanks!
  • Question
    Why is pi irrational?
    Top Answerer
    Pi is irrational because its value cannot be exactly expressed as a fraction (that is, a ratio of integers). 22/7 is often used as an expression of pi, but it is only an approximation of the true value. Even 3.14159 is only an approximation of pi's value (which is actually a seemingly endless decimal).
    Thanks!
  • Question
    How do I find the circumference of a circle that has an area of 452.16 square meters?
    Top Answerer
    Divide the area by pi. That's the square of the radius. Find the square root. That's the radius. Double it. That's the diameter. Multiply by pi. That's the circumference.
    Thanks!
  • Question
    How do I find the circumference given the area of the circle in terms of pi?
    Top Answerer
    Divide the area by pi to get the square of the radius. Take the square root to get the radius. Double it to get the diameter. Multiply by pi to get the circumference.
    Thanks!
  • Question
    How do I calculate the area of a circle with a given circumference?
    wikiHow Contributor
    Community Answer
    Remember these; a=2πr, and C=πr². First you need to find the square root of the circumference, and then divide that by π. This will be the radius of the circle, and then you simply find the area using the formula. Using algebraic rulings, you can also do this backwards, from the area to the circumference.
    Thanks!
  • Question
    How am I supposed to solve for the circumference and area, if the radius they gave me was x+1?
    Top Answerer
    Treat that radius as if it were an actual number. To find the circumference, you double the radius and multiply by pi. To find the area, you square the radius and multiply by pi.
    Thanks!
  • Question
    How can I do this in centimeters?
    wikiHow Contributor
    Community Answer
    Centimeters are a unit of measurement. You do the same math, and it is simply in the centimeters unit.
    Thanks!
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Quick Summary

To find the circumference of a circle, take its diameter times pi, which is 3.14. For example, if the diameter of a circle is 10 centimeters, then its circumference is 31.4 centimeters. If you only know the radius, which is half the length of the diameter, you can take the radius times 2 pi, or 6.28. In the example above, the radius would be 5 centimeters, so 5 centimeters times 6.28 is the same 31.4 centimeters.

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Date: 01.12.2018, 21:37 / Views: 92385