Solve problems involving circles

Circumference and Area of a Circle

5.3

Circumference and Area of a Circle

	Definition

	The circumference of a circle is the measurement around a circle.

Relationship between circumference and diameter:

(i)			\(\dfrac{\text{Circumference}}{\text{Diameter}}= \pi\), where \(\pi = 3.142\) or \(\pi=\dfrac{22}{7}\)

(ii)			\(\begin{aligned} \text{Circumference} &= \pi \times \text{diameter} \\&=\pi d\end{aligned}\)

(iii)			\(\begin{aligned} \text{Circumference} &= \pi \times 2 \times \text{radius}\\&=2\pi r \end{aligned}\)

Area of a Circle:

\(\text{Area of circle} = \pi r^2\)

Length of Arc in a Circle:

\(\begin{aligned}\dfrac{\text{Length of arc}}{\text{Circumference}} &= \dfrac{\text{Angle at centre}}{360 ^{\circ}} \\\\\dfrac{\text{Length of arc}}{2\pi r}&=\dfrac{\theta}{360 ^{\circ}} \end{aligned}\)

Area of a Sector:

\(\begin{aligned}\dfrac{\text{Area of sector}}{\text{Area of circle}} &= \dfrac{\text{Angle at centre}}{360 ^{\circ}}\\\\\dfrac{\text{Area of sector}}{\pi r^2} &= \dfrac{\theta}{360 ^{\circ}}\end{aligned}\)

Circumference and Area of a Circle

5.3

Circumference and Area of a Circle

	Definition

	The circumference of a circle is the measurement around a circle.

Relationship between circumference and diameter:

(i)			\(\dfrac{\text{Circumference}}{\text{Diameter}}= \pi\), where \(\pi = 3.142\) or \(\pi=\dfrac{22}{7}\)

(ii)			\(\begin{aligned} \text{Circumference} &= \pi \times \text{diameter} \\&=\pi d\end{aligned}\)

(iii)			\(\begin{aligned} \text{Circumference} &= \pi \times 2 \times \text{radius}\\&=2\pi r \end{aligned}\)

Area of a Circle:

\(\text{Area of circle} = \pi r^2\)

Length of Arc in a Circle:

\(\begin{aligned}\dfrac{\text{Length of arc}}{\text{Circumference}} &= \dfrac{\text{Angle at centre}}{360 ^{\circ}} \\\\\dfrac{\text{Length of arc}}{2\pi r}&=\dfrac{\theta}{360 ^{\circ}} \end{aligned}\)

Area of a Sector:

\(\begin{aligned}\dfrac{\text{Area of sector}}{\text{Area of circle}} &= \dfrac{\text{Angle at centre}}{360 ^{\circ}}\\\\\dfrac{\text{Area of sector}}{\pi r^2} &= \dfrac{\theta}{360 ^{\circ}}\end{aligned}\)