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Door 9 · Grade 7

📐 Circles (Basics)

radius (r) = half of diameter: r = d/2

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Radius, Diameter, Chord, Circumference, Area

A circle is the set of all points equidistant from a fixed center point.
TermDefinitionFormulaRadius (r)Distance from center to edger = d / 2Diameter (d)Distance across circle through centerd = 2rChordLine segment joining any two points on circle—Circumference (C)Distance around the circleC = 2r = dArea (A)Space enclosed by the circleA = r²Value of pi: 3.14159... or 22/7 (approx). Use 22/7 when radius is a multiple of 7.
Semicircle: Area = r²/2, Perimeter = r + 2r
Quarter circle: Area = r²/4, Perimeter = r/2 + 2r

Worked example

Problem: Circle radius = 7cm. Find diameter, circumference, area. (use pi = 22/7)

  1. d = 2 x 7 = 14cm.
  2. C = 2 x 22/7 x 7 = 44cm.
  3. A = 22/7 x 7 x 7 = 154cm².

Answer: A = 22/7 x 7 x 7 = 154cm².