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Circumference and Area Formulas for Circles: Helpful Information

Learn about calculating circumference and area of circles, including formulas, use of π (pi), and practical examples with step-by-step solutions.

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Circumference and Area Formulas for Circles: Helpful Information

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  1. Circumference and Area

  2. Information

  3. The formula for circumference The circumference is thedistance around the outside of the circle. For any circle, the ratio between the circumference, C, and the diameter, d, is always the same number. C π= This number is called π (pi). d C = πd Rearrange this to get: So, for a circle of diameter, d, and radius, r: circumference = 2πr = πd or

  4. The value of π The symbol π is used because pi is an irrational number. It cannot be written exactly. When performing calculations involving the value π, an approximation for the value is required. • for a rough approximation use 3. 22 • better approximations are 3.14 or . 7 • the π button on a calculator can also be used. Most questions will indicate which approximation to use. When calculating formulas, write π as a symbol throughout and evaluate the expression at the end.

  5. Finding the circumference Jess is wrapping paper towel tubes for party decorations. She needs to enough wrapping paper for 6 tubes. Use π = 3.14 to find the length of wrapping paper needed. Find the length of wrapping paper needed for one tube: C = πd write the formula for circumference, C: substitute for the values given: = 3.14 × 1.25 Diameter, d =1.25inches evaluate: = 9.925in Multiply your answer by the number of tubes: 9.925 × 6= 23.55in

  6. More circumferences

  7. Formula for the area of a circle The area of a circle can be found by dividing it into sectors and rearranging the pieces to form a parallelogram. radius, r radius, r half the circumference area of parallelogram = base × height C base ≈ half the circumference, 2 height ≈ radius, r C Therefore, the area of circle ≈∙r 2

  8. Formula for the area of a circle radius, r half the circumference C circumference, C= 2πr area of circle, A≈∙r 2 C = πr A ≈πr∙r 2 A ≈πr2 The more sectors the circle is divided into, the more accurate the approximation becomes. area of circle Therefore, for a circle of radius, r: A = πr2

  9. Finding the area of a circle Esteban is buying a cover for his circular pool. Use π = 3.14 to find the area of the cover he needs. write the formula for the area, A, of a circle: A = πr2 substitute for the values given: = 3.14 × 72 evaluate exponent: = 3.14 × 49 7feet evaluate: = 153.86feet2 rounding: = 154feet2

  10. Finding the area using the diameter Use π = 3.14 to find the area of glass needed to replace this circular window. d r = write the formula for the radius, r, of a circle: 2 20in substitute for the values given: r = 2 r = 10in evaluate: write the formula for the area, A, of a circle: A = πr2 20inches substitute for the values given: = 3.14 × (10in)2 evaluate: = 314in2

  11. More areas

  12. Sort the formulas

  13. Running track 100m • This running track has 6 lanes that are each 1m wide. • The straight sections of the 6 lanes are 100m long. • The total width of the track is 100m. For a fair one-lap race, how far must the runner on the outside lane start in front of the runner on the inside lane?

  14. Running track solution The runner in the outside lane needs to start 510.86 – 479.46 = 31.4m in front of the runner in the inside lane.

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