004 area of circles

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004 area of circles

  1. 1. GT Geometry Drill 4.03 4/11/13 Turn in CW/HWWarm UpFind the unknown side lengths in each specialright triangle.1. a 30°-60°-90° triangle with hypotenuse 2 ft2. a 45°-45°-90° triangle with leg length 4 in.3. a 30°-60°-90° triangle with longer leg length 3m
  2. 2. April is Math MonthNow for today’s question:Alice Spent 1/3 of her money at a store and then loaned ¾ of what remained to a friend. If she still had $2 remaining, how many dollars did she originally have?We will review April 11- 20 on this Friday do you have all the answers?
  3. 3. ObjectivesDevelop and apply the formulas for thearea and circumference of a circle.Develop and apply the formula for thearea of a regular polygon.
  4. 4. Vocabularycirclecenter of a circlecenter of a regular polygonapothemcentral angle of a regular polygon
  5. 5. A circle is the locus of points in a plane that are afixed distance from a point called the center of thecircle. A circle is named by the symbol  and itscenter. A has radius r = AB and diameter d = CD.The irrational number is defined as the ratio ofthe circumference C tothe diameter d, orSolving for C gives the formulaC = d. Also d = 2r, so C = 2r.
  6. 6. You can use the circumference of a circle to find itsarea. Divide the circle and rearrange the pieces tomake a shape that resembles a parallelogram. The base of the parallelogram is about half the circumference, or r, and the height is close to the radius r. So A   r · r =  r2. The more pieces you divide the circle into, the more accurate the estimate will be.
  7. 7. Example 1A: Finding Measurements of CirclesFind the area of K in terms of . A = r2 Area of a circle. A = (3)2 Divide the diameter by 2 to find the radius, 3. A = 9 in2 Simplify.
  8. 8. Example 1B: Finding Measurements of CirclesFind the radius of J if the circumference is(65x + 14) m. C = 2r Circumference of a circle(65x + 14) = 2r Substitute (65x + 14) for C. r = (32.5x + 7) m Divide both sides by 2.
  9. 9. Example 1C: Finding Measurements of CirclesFind the circumference of M if the area is25 x2 ft2Step 1 Use the given area to solve for r. A = r2 Area of a circle 25x2 = r2 Substitute 25x2 for A. 25x2 = r2 Divide both sides by . Take the square root of 5x = r both sides.
  10. 10. Example 1C ContinuedStep 2 Use the value of r to find the circumference. C = 2r C = 2(5x) Substitute 5x for r. C = 10x ft Simplify.
  11. 11. Check It Out! Example 1Find the area of A in terms of  in whichC = (4x – 6) m. A = r2 Area of a circle. Divide the diameter by 2 A = (2x – 3)2 m to find the radius, 2x – 3. A = (4x2 – 12x + 9) m2 Simplify.
  12. 12. Helpful HintThe  key gives the best possibleapproximation for  on your calculator.Always wait until the last step to round.
  13. 13. Example 2: Cooking ApplicationA pizza-making kit contains three circularbaking stones with diameters 24 cm, 36 cm,and 48 cm. Find the area of each stone. Roundto the nearest tenth.24 cm diameter 36 cm diameter 48 cm diameterA = (12)2 A = (18)2 A = (24)2 ≈ 452.4 cm2 ≈ 1017.9 cm2 ≈ 1809.6 cm2
  14. 14. Check It Out! Example 2A drum kit contains three drums with diametersof 10 in., 12 in., and 14 in. Find the circumferenceof each drum.10 in. diameter 12 in. diameter 14 in. diameter C = d C = d C = d C = (10) C = (12) C = (14) C = 31.4 in. C = 37.7 in. C = 44.0 in.
  15. 15. Lesson Quiz: Part IFind each measurement.1. the area of D in terms of  A = 49 ft22. the circumference of T in which A = 16 mm2 C = 8 mm
  16. 16. Lesson Quiz: Part IIFind each measurement.3. Speakers come in diameters of 4 in., 9 in., and 16 in. Find the area of each speaker to the nearest tenth. A1 ≈ 12.6 in2 ; A2 ≈ 63.6 in2 ; A3 ≈ 201.1 in2Find the area of each regular polygon to thenearest tenth.4. a regular nonagon with side length 8 cm A ≈ 395.6 cm25. a regular octagon with side length 9 ft A ≈ 391.1 ft2

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