Sec 3 · G1 (N(T))

Arc length and sector area

Practise arc length and sector area with step-by-step help. Free account.

1. Arc length

	$\theta$ in degrees
Arc length	$\dfrac{\theta}{360} \times 2\pi r$
Perimeter of a sector	$2r + \dfrac{\theta}{360} \times 2\pi r$

Degrees: r = 7 cm, θ = 40°

\displaystyle s = \dfrac{\theta}{360} \times 2\pi r

e.g.

\displaystyle s = \dfrac{40}{360} \times 2\pi(7)

\displaystyle s = \dfrac{14\pi}{9}

\displaystyle s = 4.89\text{ (3 s.f.)}

📖 Worked example

A sector of a circle has radius $4$ cm and angle $150^\circ$ . Find the length of its arc, correct to 3 significant figures.

Step 1 of 2

The arc is a fraction of the circumference

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{150}{360} \times 2\pi(4)

	$\theta$ in degrees
Sector area	$\dfrac{\theta}{360} \times \pi r^{2}$

📖 Worked example

A sector of a circle has radius $4$ cm and angle $225^\circ$ . Find its area, correct to 3 significant figures.

Step 1 of 2

The sector is a fraction of the circle

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{225}{360} \times \pi(4)^2

Practise arc length and sector area with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

1. Arc length

	$\theta$ in degrees
Arc length	$\dfrac{\theta}{360} \times 2\pi r$
Perimeter of a sector	$2r + \dfrac{\theta}{360} \times 2\pi r$

Degrees: r = 7 cm, θ = 40°

\displaystyle s = \dfrac{\theta}{360} \times 2\pi r

e.g.

\displaystyle s = \dfrac{40}{360} \times 2\pi(7)

\displaystyle s = \dfrac{14\pi}{9}

\displaystyle s = 4.89\text{ (3 s.f.)}

📖 Worked example

A sector of a circle has radius $4$ cm and angle $150^\circ$ . Find the length of its arc, correct to 3 significant figures.

Step 1 of 2

The arc is a fraction of the circumference

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{150}{360} \times 2\pi(4)

Practise this →

2. Sector area

	$\theta$ in degrees
Sector area	$\dfrac{\theta}{360} \times \pi r^{2}$

📖 Worked example

A sector of a circle has radius $4$ cm and angle $225^\circ$ . Find its area, correct to 3 significant figures.

Step 1 of 2

The sector is a fraction of the circle

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{225}{360} \times \pi(4)^2

Practise this →