Arcs and Sectors

A sector has radius 3 cm. The angle at its centre is 120°. Find:
  (a)  the arc length
  (b)  the sector area.
Use 3.14 as an approximation of $\displaystyle \pi.$

A sector has radius 50 cm. The angle at its centre is 72°. Find:
  (a)  the arc length
  (b)  the sector area.
Use 3.14 as an approximation of $\displaystyle \pi.$

The pendulum of a clock swings along an arc of a circle, centre O.

The pendulum swings through an angle of 65°, travelling from A to B.
The length of the arc AB is 28.4 centimetres.
Calculate the length of the pendulum.

The diagram shows a sector of a circle, centre C.

The radius of the circle is 20 centimetres and angle ACB is $\displaystyle 45^{\circ}$.
Calculate the area of the sector.
Take $\displaystyle \pi=3\cdot14$.

The diagram shows part of a circle, centre O.
The radius of the circle is 6.4 cm.
Major arc AB has length 31.5 cm.

Calculate the size of the reflex angle AOB.

The diagram below shows a sector of a circle, centre C.

The radius of the circle is 7.4 centimetres.
Angle ACB is $\displaystyle 320^{\circ}$.
Calculate the length of the major arc AB.

The diagram below shows a sector of a circle, centre C.

The radius of the circle is 30 centimetres.
Calculate the length of the major arc AB.
Take $\displaystyle \pi=3\cdot14.$

The diagram shows part of a football pitch.

The penalty spot is marked at point C.
AB is an arc of a circle, centre C, radius 9.15 metres.
Calculate the length of the arc AB.

The diagram shows a sector of a circle, centre C.

The radius of the circle is 12 centimetres.
The length of arc AB is 15 centimetres.
Calculate the area of the sector.

A party hat is made in the shape of a cone, as shown.

The piece of card used for making the hat is a sector of a circle, centre C.

The radius of the circle is 15 centimetres and angle ACB is 170°.
Calculate the area of the sector.