how do you find the circumference of a circle with the diameter

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A circumvolve is the set of all points in a plane that are a fixed distance, called the radius, from a fixed indicate, called the eye. ^[1] The circumference (C) of a circumvolve is its perimeter, or the altitude around it.^[2] The surface area (A) of a circle is how much infinite the circle takes up or the region enclosed by the circle.^[3] Both area and perimeter can be calculated with simple formulas using the radius or diameter of the circle and the value of pi.

1. 1

   Learn the formula for circumference. There are two formulas that tin can be used to calculate the circumference of a circle: C = 2πr or C = πd, where π is the mathematical constant approximately equal to three.14,^[4] r is equal to the radius, and d is equal to the diameter.^[5]

   • Because the radius of a circle is equal to twice its diameter, these equations are substantially the same.
   • The units for circumference can exist whatever unit of measurement for the measure of length: anxiety, miles, meters, centimeters, etc.

2. two

   Understand the dissimilar parts of the formula. There are three components to finding circumference of a circle: radius, diameter, and π. The radius and bore are related: the radius is equal to one-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 bespeak on the circle to another straight opposite it, going through the circumvolve's middle.^[6]
   • The Greek letter pi (π) represents the ratio of the circumference divided past the bore and is represented by the number iii.14159265…, an irrational number that has neither a terminal digit nor a recognizable blueprint of repeating digits.^[vii] This number is commonly rounded to 3.fourteen for basic calculations.

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3. iii

   Measure the radius or diameter of the circle. Using a ruler, place one end at i side of the circle and place it through the heart point to the other side of the circumvolve. The distance to the eye of the circle is the radius, while the distance to the other end of the circle is the diameter.

   • In most textbook math issues, the radius or diameter is given to you.

4. four

   Plug in the variables and solve. One time y'all have adamant the radius and/or diameter of the circle, y'all tin plug these variables into the appropriate equation. If you have the radius, use C = 2πr, but if y'all have the bore, use C = πd.

   • For instance: 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 = (two*three*π) = 6π = 18.84 cm
   • For instance: What is the circumference of a circumvolve with a bore of 9 thou?
     • Write the formula: C = πd
     • Plug in the variables: C = 9π
     • Multiply through: C = (ix*π) = 28.26 one thousand

5. 5

   Practice with a few examples. Now that y'all've learned the formula, it's time to practice with a few examples. The more problems you lot solve, the easier information technology 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 x ft.
     • C = 2πr = C = 2π10 = ii * x * π = 62.eight ft.

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1. i

   Larn the formula for area of a circle. The area of a circle can be calculated using the diameter or the radius with 2 different formulas: A = πrⁱⁱ or A = π(d/2)² , where π is the mathematical constant approximately equal to iii.14,^[8] r is equal to the radius, and d is the bore.^[nine]

   • Because the radius of a circumvolve is equal to half its diameter, these equations are essentially the same.
   • The units for area tin can be whatever unit for the mensurate of length squared: anxiety squared (ft²), meters squared (mⁱⁱ), centimeters squared (cm²), etc.

2. 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 bore, while the diameter is equal to double the radius.

   • The radius (r) of a circle is the distance from ane point on the circumvolve to the middle of the circle.
   • The diameter (d) of a circle is the altitude from one point on the circle to another directly opposite it, going through the circumvolve's center.^[10]
   • The Greek letter pi (π) represents the ratio of the circumference divided by the bore and is represented by the number 3.14159265…, an irrational number that has neither a final digit nor a recognizable pattern of repeating digits.^[11] This number is commonly rounded to three.14 for bones calculations.

3. 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 circumvolve. The distance to the center of the circle is the radius, while the distance to the other end of the circle is the bore.

   • In nigh textbook math problems, the radius or diameter is given to y'all.

4. 4

   Plug in the variables and solve. In one case you have determined the radius and/or bore of the circle, you lot tin plug these variables into the advisable equation. If you accept the radius, use A = πr^two , but if you take the diameter, use A = π(d/2)² .

   • For instance: What is the surface area of a circumvolve with a radius of iii one thousand?
     • Write the formula: A = πrⁱⁱ
     • Plug in the variables: A = π3²
     • Square the radius: r² = 3² = ix
     • Multiply past pi: A = 9π = 28.26 m²
   • For example: What is the expanse of a circumvolve with a diameter of 4 chiliad?
     • Write the formula: A = π(d/ii)^two
     • Plug in the variables: A = π(4/2)²
     • Divide the diameter past 2: d/2 = four/two = 2
     • Square the event: two² = iv
     • Multiply past pi: A = 4π = 12.56 m²

5. 5

   Practice with a few examples. Now that you've learned the formula, it'due south fourth dimension to practise with a few examples. The more than problems yous solve, the easier it becomes to solve them in the future.

   • Find the area of a circumvolve with a diameter of 7 ft.
     • A = π(d/2)² = π(7/ii)² = π(three.five)² = 12.25 * π= 38.47 ftⁱⁱ.
   • Discover the surface area of a circle with a radius of 3 ft.
     • A = πr^two = π3² = nine * π = 28.26 ft²

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1. 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 = (10 + seven) or d = (x + 3). In this example, you can still solve for the expanse or circumference, but your final answer will also accept that variable in it. Write downward the radius or diameter as it is stated in the problem.

   • For example: Calculate the circumference of a circle with a radius of (ten = ane).

2. 2

   Write the formula with the information given. Whether you are solving for area or circumference, you lot volition still follow the basic steps of plugging in what you know. Write down the formula for expanse or circumference and then write in the variables given.

   • For case: Calculate the circumference of a circumvolve with a radius of (x + 1).
   • Write the formula: C = 2πr
   • Plug in the given information: C = 2π(x+1)

3. 3

   Solve every bit if the variable were a number. At this point, you can just solve the trouble every bit you normally would, treating the variable equally if it were just another number. Y'all may demand to use the distributive holding to simplify the final answer.

   • For example: Summate the circumference of a circumvolve with a radius of (x = ane).
   • C = 2πr = 2π(x+i) = 2πx + 2π1 = 2πx +2π = 6.28x + six.28
   • If you are given the value of "x" after in the problem, you can plug it in and go a whole number respond.

4. four

   Practice with a few examples. Now that you've learned the formula, it'due south fourth dimension to do with a few examples. The more bug yous solve, the easier information technology becomes to solve them in the future.

   • Find the area of a circle with a radius of 2x.
     • A = πr^two = π(2x)^two = π4xⁱⁱ = 12.56x²
   • Find the surface area of a circumvolve with a bore of (ten + 2).
     • A = π(d/ii)² = π((ten +2)/2)^two = ((10 +two)²/4)π

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Add New Question

• Question

  How practise we figure circumference if the area of a circle is 3.fourteen cm squared?

  

  Divide the surface area by pi; that gives you r ². Find the square root; that gives y'all r. Double it; that gives you the bore. Multiply past pi; that gives you lot the circumference.

• Question

  How exercise I find the expanse of a circle when I have the circumference?

  

  Pi x diameter = Pi ten (ii x radius) = Circumference So: Radius = Circumference/(2xPi) Once you accept the radius, apply this formula: Expanse = Pi x radius^two

• Question

  How do I find the circumference of a circle that has an area of 452.16 square meters?

  

  Carve up the area by pi. That'southward the square of the radius. Find the square root. That's the radius. Double information technology. That'south the diameter. Multiply by pi. That's the circumference.

• Question

  How practise I find the circumference given the surface area of the circle in terms of pi?

  

  Divide the expanse past pi to get the foursquare of the radius. Take the square root to get the radius. Double it to get the bore. Multiply by pi to get the circumference.

• Question

  If the radius of a circle is 15.3 centimeters, so what is the bore?

  

  The diameter is twice the radius.

• Question

  Why is pi irrational?

  

  Pi is irrational considering its value cannot be exactly expressed as a fraction (that is, a ratio of integers). 22/seven is oftentimes used as an expression of pi, but it is only an approximation of the true value. Even iii.14159 is but an approximation of pi's value (which is actually an apparently endless decimal number).

• Question

  How practice I summate the area of a circumvolve with a given circumference?

  

  Call up these; a=2πr, and C=πr². Get-go yous demand to find the square root of the circumference, and then split up that past π. This volition be the radius of the circle, and then you lot only find the area using the formula. Using algebraic rulings, you tin can likewise do this backwards, from the area to the circumference.

• Question

  How do I discover 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 circumvolve equals the length of the square side. Only multiply the diameter past pi, and yous accept your circumference!

• Question

  How am I supposed to solve for the circumference and area, if the radius they gave me was x+1?

  

  Treat that radius as if it were an actual number. To find the circumference, yous double the radius and multiply past pi. To find the area, you foursquare the radius and multiply by pi.

• Question

  How do I find the diameter of a circumvolve whose area is 28.26?

  

  Carve up the area by pi: that'southward the square of the radius. Find the foursquare root: that's the radius. Double it: that'southward the diameter.

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Article Summary Ten

To find the circumference of a circle, take its diameter times pi, which is 3.fourteen. For example, if the diameter of a circumvolve is 10 centimeters, then its circumference is 31.4 centimeters. If you only know the radius, which is half the length of the diameter, yous can take the radius times two pi, or 6.28. In the example in a higher place, the radius would be five centimeters, and so 5 centimeters times 6.28 is the same 31.4 centimeters. For more tips on finding the circumference and expanse of a circle, even if it includes variables, read on!

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Source: https://www.wikihow.com/Find-the-Circumference-and-Area-of-a-Circle

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