Any Way You Slice It

1
Any Way You Slice It

• Some additional definitions for sections of a
  circle
• A sector of a circle is the region between two
  radii of a circle and the included arc (similar
  to a slice of pizza)
• A segment of a circle is the region between a
  chord of a circle and the included arc
• An annulus is the region between two concentric
  circles (similar to a ring or washer)
• How can you apply the area formulas discovered so
  far in this chapter to find formulas for the
  areas of these sections of a circle?

2
Any Way You Slice It

• The area of a sector of a circle is found using
  the same approach as that used for arc length
• The fraction of the circle covered by the sector
  equals the arc measure divided by 360
• The whole circle has an area of pr2
• Multiplying the area of the circle by the
  fraction of the circle included in the sector
  gives the formula
• Asector (a / 360) pr2

3
Any Way You Slice It

• The area of a segment of a circle is part of the
  area of a sector intercepted by the chord
• The chord cuts off an arc that can be used to
  find the area of the corresponding sector
• A triangle is created by the chord and the two
  radii to the endpoints of the chord
• The base of the triangle is the length of the
  chord
• The height of the triangle is the distance
  between the chord and the center of the circle
• Subtracting the area of the triangle from the
  area of the sector gives the formula
• Asegment pr2 a / 360 - ½bh

4
Any Way You Slice It

• The area of an annulus of a circle is the area
  between the inner and outer circles
• The area of each concentric circle is p times the
  radius squared
• The area between the circles is the area of the
  outer circle minus the area of the inner circle
• Let the radius of the outer circle be R, and the
  radius of the inner circle be r
• Subtracting the area of the inner circle from the
  area of the outer circle gives the formula
• Aannulus pR2 - pr2 or Aannulus p(R2 - r2)