AREAS OF CIRCLES, SECTORS, SEGMENTS, AND ELLIPSES

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UNIT 27

• AREAS OF CIRCLES, SECTORS, SEGMENTS, AND ELLIPSES

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AREAS OF CIRCLES

• The area of a circle is equal to the product of ?
  and the square of the radius (A ?r2)
• The areas of two circles have the same ratio as
  the squares of the radii or diameters

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AREAS OF CIRCLES

• The areas of two circles are 144 mm2 and 36 mm2.
  Compare the radius of the larger circle with the
  radius of the smaller circle

• The radius of the larger circle is 2 times larger
  than the radius of the smaller circle

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AREAS OF SECTORS

• A sector of a circle is a figure formed by two
  radii and the arc intercepted by the radii
• The area of a sector is given as
• Determine the area of a sector of a circle with a
  central angle of 48 and a radius of 2.75 feet

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AREAS OF SEGMENTS

• A segment of a circle is a figure formed by an
  arc and the chord joining the end points of the
  arc
• The area of a segment is found by subtracting the
  area of a triangle from the area of a sector
• Find the area of segment ACB in the figure below,
  given that ?AOB 85?, the radius of the circle
  is 4 in, and AB is 10 in

• Area of the sector

A (85/360)?(4")2 11.868 in2

• Area of the triangle

A ½ bh ½ (10")(2") 10 in2

• Area of the segment

A 11.868 in2 10 in2 1.868 in2 Ans
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AREAS OF ELLIPSES

• An ellipse is a closed oval-shaped curve that is
  symmetrical to two lines or axes that are
  perpendicular to each other
• The longer axis is called the major axis and the
  shorter axis is called the minor axis
• The area of an ellipse is equal to the product of
  ? and one half the major axis and one half the
  minor axis
• Find the area of an ellipse that is 12 feet long
  (major axis) and 9 feet wide (minor axis)

• Area ?(12 ft ? 2)(9 ft ? 2) 84.823 ft2 Ans

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PRACTICE PROBLEMS

• 1. Find the area of a circle that has a radius
  of 7.25 meters.
• 2. Determine the radius of a circular patio
  which is to have an area of 14 square yards.
• 3. The radii of two circles are 6 inches and 2
  inches. Compare the area of the larger circle
  with the area of the smaller circle.
• 4. Find the area of the sector of a circle with
  a central angle of 78 and a radius of 4.5
  inches.
• 5. Determine the central angle for a sector of a
  circle with a 3- meter radius given that the area
  of the sector is 3.77 square meters.

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PRACTICE PROBLEMS

• 6. Find the area of a segment of a circle given
  a central angle of 60 and a radius of 4 inches
  when the height and base of the triangular
  section are 2 inches and 3 inches respectively.
• 7. Determine the area of an ellipse with a major
  axis of 7.5 cm and a minor axis of 5.5 cm.
• 8. Determine the major axis of an ellipse if its
  area is 236.34 square yards and the minor axis is
  12.3 yards.

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PROBLEM ANSWER KEY

• 1. 165.13 m2
• 2. 2.111 yards
• 3. The area of the larger circle is 9 times
  larger than the area of the smaller circle
• 4. 13.784 in2
• 5. 48
• 6. 5.378 in2
• 7. 32.4 cm2
• 8. 24.465 yards