Content

• To step
• Method 1 of 2: Using the circumference equation
• Method 2 of 2: Fix the problem in reverse

The formula for calculating the circumference (C) of a circle, C = πD or C = 2πR, is simple if you know the diameter (D) or the radius (R) of the circle. But what do you do if you only know the area of ​​the circle? Like many things in mathematics, there are multiple solutions to this problem. The formula C = 2√πA is designed to find the circumference of a circle using the area (A). You can also solve the equation A = πR in reverse order to find R, and then enter R into the perimeter equation. Both comparisons give the same result.

To step

Method 1 of 2: Using the circumference equation

1. Use the formula C = 2√πA to solve the problem. This formula calculates the circumference of a circle if you only know its area. C stands for the perimeter and A for the area. Write this formula to start solving the problem.
   • The π symbol, which stands for pi, is a repeating decimal with (now) thousands of digits after the comma. For simplicity, use 3.14 as the value of pi.
   • Since you need to convert pi to its numeric form anyway, use 3.14 in the equation from the beginning. Write it as C = 2√3.14 x A.
2. Process the area as A in the equation. Since you already know the area of ​​the circle, that's the value of A. Then continue to solve the problem using the order of the operations.
   • Let's say the area of ​​the circle is 500 cm. Then you work out the equation as follows: 2√3.14 x 500.
3. Multiply pi by the area of ​​the circle. In the order of the operations, the operations within the square root symbol come first. Multiply pi by the area of ​​the circle you plugged in. Then connect that result to the equation.
   • If the calculation equals 2√3.14 x 500, then you calculate 3.14 x 500 = 1570 first. Then calculate 2√1.570.
4. Particular square root of the sum. There are several ways to calculate the square root. If you're using a calculator, press the function √ and type in the number. You can also solve the problem by hand using prime factors.
   • The square root of 1570 is 39.6.
5. Multiply the square root by 2 to find the circumference. Finally, you complete the calculation by multiplying the result by 2. This returns a final number, the circumference of the circle.
   • Calculate 39.6 x 2 = 79.2. This means that the circumference is 79.2 cm, which solves the formula.

Method 2 of 2: Fix the problem in reverse

1. Use the formula A = πR in. This is the formula for the area of ​​a circle. A stands for the area and R for the radius. Normally you would use it if you knew the radius, but you can also fill in the area to solve the equation.
   • Again, use 3.14 as the rounded value for pi.
2. Enter the area as the value for A. Use the area of ​​the circle in the equation. Place this to the left of the equation as the value for A.
   • Suppose the area of ​​the circle is 200 cm. The equation then becomes 200 = 3.14 x R.
3. Divide both sides of the equation by 3.14. To solve these kinds of equations, you have to gradually eliminate the steps on the right by doing the opposite operations. Since you know the value of pi, divide each side by that value. This eliminates pi on the right, and gives you a new numeric value on the left.
   • If you divide 200 by 3.14, the result is 63.7. So the new equation is 63.7 = R.
4. Particular square root of the result to get the radius of the circle. Then the exponent to the right of the equation is eliminated. The opposite of "exponentiation" is finding the square root of the number. Find the square root of each side of the equation. This will eliminate the exponent on the right and the radius will be on the left.
   • The square root of 63.7 is 7.9. The equation then becomes 7.9 = R, which means that the circle's radius is 7.9. This will give you all the information you need to find the outline.
5. Determine the circumference of the circle using the radius. There are two formulas to find the perimeter (C). The first is C = πD, where D is the diameter. Multiply the radius by 2 to find the diameter. The second is C = 2πR. Multiply 3.14 by 2 and then multiply the result by the radius. Both formulas will give you the same result.
   • Use the first option, 7.9 x 2 = 15.8, the diameter of the circle. This diameter times 3.14 is 49.6.
   • For the second option, the calculation becomes 2 x 3.14 x 7.9. First you calculate 2 x 3.14 = 6.28, and that multiplied by 7.9 is 49.6. Notice how both methods give you the same answer.