How Do You Find the Area of a Circle When You Know the Circumference

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A circle is the set of all points in a plane that are a fixed distance, chosen the radius, from a fixed point, chosen the middle. ^[ane] The circumference (C) of a circumvolve is its perimeter, or the distance around it.^[2] The area (A) of a circumvolve is how much space the circle takes up or the region enclosed past the circle.^[3] Both area and perimeter tin 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 can be used to summate the circumference of a circle: C = 2πr or C = πd, where π is the mathematical constant approximately equal to 3.xiv,^[4] r is equal to the radius, and d is equal to the bore.^[5]

   • Because the radius of a circle is equal to twice its bore, these equations are essentially the aforementioned.
   • The units for circumference can be whatever unit of measurement for the mensurate of length: feet, miles, meters, centimeters, etc.

2. 2

   Understand the unlike parts of the formula. There are iii components to finding circumference of a circumvolve: radius, bore, and π. The radius and diameter are related: the radius is equal to half the diameter, while the bore is equal to double the radius.

   • The radius (r) of a circle is the altitude from ane indicate on the circumvolve to the centre of the circle.
   • The diameter (d) of a circumvolve is the distance from 1 point on the circle to another straight opposite it, going through the circle'south center.^[6]
   • The Greek letter of the alphabet pi (π) represents the ratio of the circumference divided by the diameter and is represented past the number 3.14159265…, an irrational number that has neither a terminal digit nor a recognizable pattern of repeating digits.^[7] This number is usually rounded to iii.14 for bones calculations.

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3. 3

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

   • In well-nigh textbook math issues, the radius or bore is given to you lot.

4. 4

   Plug in the variables and solve. In one case you have adamant the radius and/or diameter of the circle, you tin plug these variables into the appropriate equation. If you accept the radius, employ C = 2πr, only if you take the diameter, use C = 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 = (ii*3*π) = 6π = eighteen.84 cm
   • For example: What is the circumference of a circumvolve 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. 5

   Do with a few examples. Now that y'all've learned the formula, it's time to exercise with a few examples. The more problems you 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
   • Discover the circumference of a circumvolve with a radius of ten ft.
     • C = 2πr = C = 2π10 = 2 * ten * π = 62.8 ft.

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1. 1

   Learn the formula for surface area of a circle. The expanse of a circle can be calculated using the diameter or the radius with two different formulas: A = πr² or A = π(d/2)² , where π is the mathematical abiding approximately equal to iii.14,^[8] r is equal to the radius, and d is the bore.^[9]

   • Because the radius of a circle is equal to one-half its diameter, these equations are essentially the same.
   • The units for area can be any unit for the measure of length squared: anxiety squared (ft^two), meters squared (chiliad²), centimeters squared (cm²), etc.

2. 2

   Understand the different parts of the formula. There are three components to finding circumference of a circle: radius, bore, 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 altitude from ane point on the circle to the center of the circle.
   • The diameter (d) of a circumvolve is the distance from one signal on the circumvolve to another directly contrary it, going through the circle's center.^[ten]
   • The Greek letter pi (π) represents the ratio of the circumference divided past the diameter and is represented by the number iii.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 identify 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. 4

   Plug in the variables and solve. In one case you lot have determined the radius and/or diameter of the circle, you tin can plug these variables into the advisable equation. If you have the radius, apply A = πr² , but if you take the diameter, utilise A = π(d/2)² .

   • For example: What is the area of a circumvolve with a radius of 3 m?
     • Write the formula: A = πr²
     • Plug in the variables: A = π3²
     • Square the radius: r² = three² = nine
     • Multiply past pi: A = 9π = 28.26 m²
   • For example: What is the area of a circle with a diameter of four g?
     • Write the formula: A = π(d/2)²
     • Plug in the variables: A = π(iv/2)²
     • Carve up the diameter by two: d/two = 4/2 = two
     • Square the result: 2² = 4
     • Multiply past pi: A = 4π = 12.56 chiliad²

5. five

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

   • Observe the area of a circle with a bore of 7 ft.
     • A = π(d/2)^two = π(7/2)^two = π(iii.5)ⁱⁱ = 12.25 * π= 38.47 ft².
   • Find the surface area of a circumvolve with a radius of iii ft.
     • A = πr² = π3² = 9 * π = 28.26 ft^two

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1. 1

   Make up one's mind the radius or bore of the circle. Some bug may give y'all a radius or diameter that has a variable in it: r = (x + 7) or d = (ten + 3). In this case, you can nonetheless solve for the area or circumference, but your final answer will also have that variable in it. Write down the radius or diameter as information technology is stated in the problem.

   • For case: Calculate the circumference of a circle with a radius of (x = 1).

2. two

   Write the formula with the data given. Whether you are solving for area or circumference, you will still follow the bones steps of plugging in what yous know. Write down the formula for area or circumference 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+ane)

3. 3

   Solve as if the variable were a number. At this bespeak, you tin can just solve the problem as you normally would, treating the variable as if it were just some other number. Yous may need to use the distributive belongings to simplify the final answer.

   • For example: Calculate the circumference of a circle with a radius of (x = 1).
   • C = 2πr = 2π(x+ane) = 2πx + 2π1 = 2πx +2π = half-dozen.28x + 6.28
   • If you are given the value of "x" subsequently in the problem, yous can plug it in and get a whole number answer.

4. 4

   Practice with a few examples. Now that y'all've learned the formula, information technology's time to practice with a few examples. The more than problems y'all solve, the easier it becomes to solve them in the future.

   • Discover the surface area of a circle with a radius of 2x.
     • A = πr² = π(2x)² = π4x² = 12.56xⁱⁱ
   • Discover the area of a circle with a bore of (x + 2).
     • A = π(d/ii)ⁱⁱ = π((x +2)/2)^two = ((ten +2)²/iv)π

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Add New Question

• Question

  How do nosotros figure circumference if the surface area of a circle is 3.fourteen cm squared?

  

  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 past pi; that gives y'all the circumference.

• Question

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

  

  Pi x diameter = Pi ten (2 ten radius) = Circumference Then: Radius = Circumference/(2xPi) Once you have the radius, use this formula: Expanse = Pi x radius^two

• Question

  How exercise I discover the circumference of a circle that has an surface area of 452.16 square meters?

  

  Divide the area by pi. That's the square of the radius. Observe the foursquare root. That's the radius. Double it. That's the diameter. Multiply past pi. That's the circumference.

• Question

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

  

  Split up the area by pi to get the foursquare of the radius. Have the square root to become the radius. Double it to become the bore. Multiply by pi to become the circumference.

• Question

  If the radius of a circle is 15.3 centimeters, and then what is the diameter?

  

  The diameter is twice the radius.

• Question

  Why is pi irrational?

  

  Pi is irrational because its value cannot be exactly expressed as a fraction (that is, a ratio of integers). 22/vii 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 really an apparently endless decimal number).

• Question

  How do I summate the surface area of a circle with a given circumference?

  

  Call up these; a=2πr, and C=πr². First you need to observe the square root of the circumference, and then dissever that by π. This will be the radius of the circle, and then you merely find the surface area using the formula. Using algebraic rulings, you can also do this backwards, from the expanse to the circumference.

• Question

  How practice I observe the circumference of a circle within a foursquare with merely the measurement of the square length?

  

  Shamitha Kuppala

  Customs Answer

  If the circle is touching the sides of the square, that ways that the diameter of the circle equals the length of the square side. Just multiply the bore by pi, and you accept your circumference!

• Question

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

  

  Care for that radius as if it were an bodily number. To observe the circumference, y'all double the radius and multiply by pi. To find the area, you square the radius and multiply by pi.

• Question

  How exercise I find the diameter of a circle whose surface area is 28.26?

  

  Separate the area past pi: that's the square of the radius. Notice the square root: that'south the radius. Double information technology: that'southward the bore.

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Article Summary X

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, so its circumference is 31.iv centimeters. If y'all merely know the radius, which is half the length of the bore, you tin accept the radius times 2 pi, or 6.28. In the case above, the radius would exist 5 centimeters, so 5 centimeters times 6.28 is the aforementioned 31.4 centimeters. For more tips on finding the circumference and area 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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