Circles (Basics) • Topic 1 of 1

Radius, Diameter, Chord, Circumference, Area

A circle is the set of all points equidistant from a fixed center point.

Term	Definition	Formula
Radius (r)	Distance from center to edge	r = d / 2
Diameter (d)	Distance across circle through center	d = 2r
Chord	Line segment joining any two points on circle	—
Circumference (C)	Distance around the circle	C = 2πr = πd
Area (A)	Space enclosed by the circle	A = πr²

Value of pi: π ≈ 3.14159... or 22/7 (approx). Use 22/7 when radius is a multiple of 7.

Semicircle: Area = πr²/2, Perimeter = πr + 2r

Quarter circle: Area = πr²/4, Perimeter = πr/2 + 2r

CIRCLE PARTS DIAGRAM:

              P
             /|
            / |r (radius)
           /  |
Q---------O---------R
   (diameter = 2r)

  O = center
  OP = radius (r)
  QR = diameter (d = 2r)
  PS = chord (does not pass through center)

FORMULAS:
  Circumference = 2 * pi * r  (or pi * d)
  Area          = pi * r^2
  Semicircle area = pi*r^2 / 2
  Quarter circle area = pi*r^2 / 4

Solved Examples

Worked Example

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

Solutiond = 2 x 7 = 14cm. C = 2 x 22/7 x 7 = 44cm. A = 22/7 x 7 x 7 = 154cm^2.

Worked Example

Circle circumference = 62.8cm. Find radius and area. (pi = 3.14)

Solution2 x pi x r = 62.8 => r = 62.8 / 6.28 = 10cm. A = 3.14 x 100 = 314cm^2.

Worked Example

Semicircle radius = 14cm. Find perimeter and area. (pi = 22/7)

SolutionPerimeter = pi x r + 2r = 44 + 28 = 72cm. Area = pi x r^2 / 2 = 616/2 = 308cm^2.

Key Points

radius (r) = half of diameter: r = d/2
Circumference = 2 x pi x r
Area = pi x r^2
Semicircle area = pi x r^2 / 2
Use pi = 22/7 when radius is a multiple of 7; otherwise use 3.14

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The diameter is ___ the radius.

Explanation: $d=2r$.

Q2.The circumference of a circle is:

Explanation: $2\pi r$.

Q3.The area of a circle is:

Explanation: $\pi r^2$.

Q4.The longest chord of a circle is the:

Explanation: Diameter.

Practice more MCQs → 📝 Assignment · 35 marks