Coaching Centre
Circumference, arcs and sector perimeters
Circumference of a circle, arc length as a fraction of the circumference, and perimeters of sectors, semicircles and composite shapes.
Circumference and arcs
The line shows arc length against radius for the chosen angle.
Find the perimeter of a sector with radius $6$ cm and angle $60^\circ$.
Perimeter of a sector, radius $6$ cm, angle $60^\circ$ (2 d.p.)?
$12 + 2\pi$.
Circumference of a circle with radius $5$ (2 d.p.)?
$10\pi$.
Perimeter of a semicircle with diameter $10$ (2 d.p.)?
$5\pi + 10$.
The exact arc length for radius $6$, angle $60^\circ$ is:
$\tfrac{1}{6} \times 12\pi$.
A circle has circumference $20\pi$. Find its radius.
$2\pi r = 20\pi$.
Arc length of a quarter circle of radius $14$ (2 d.p.)?
$\tfrac{1}{4} \times 28\pi = 7\pi$.
An arc of a circle with radius $8$ has length $4\pi$. Find the angle.
$\tfrac{\theta}{360} \times 16\pi = 4\pi$.
How far does the tip of a $1$ m clock hand travel in one revolution (2 d.p.)?
$2\pi \times 1$.
New numbers every time. Keep going until you get five in a row.