Exercises: Arc Length and Area of a Sector
A circle has radius $6$ cm. A sector has a central angle of $60^\circ$. Find the length of the arc, in terms of $\pi$.
A circle has radius $6$ cm. A sector has a central angle of $60^\circ$.
Find the length of the arc, in terms of $\pi$.
A circle has radius $10$ cm. A sector has a central angle of $72^\circ$. Find the area of the sector, in terms of $\pi$.
A circle has radius $10$ cm. A sector has a central angle of $72^\circ$.
Find the area of the sector, in terms of $\pi$.
A sector of a circle of radius $5$ cm has an arc length of $7$ cm. Find the central angle of the sector, correct to the nearest degree.
A sector of a circle of radius $5$ cm has an arc length of $7$ cm.
Find the central angle of the sector, correct to the nearest degree.
A circular pizza in a restaurant in Galway has a radius of $15$ cm. It is cut into $8$ equal slices. a) Find the central angle of each slice. b) Find the area of one…
A circular pizza in a restaurant in Galway has a radius of $15$ cm. It is cut into $8$ equal slices.
- a) Find the central angle of each slice.
- b) Find the area of one slice, correct to one decimal place.
- c) Find the perimeter of one slice, correct to one decimal place.
A windscreen wiper has a blade of length $40$ cm attached to a pivot. The wiper sweeps through an angle of $110^\circ$. The blade extends from $10$ cm to $50$ cm from…
A windscreen wiper has a blade of length $40$ cm attached to a pivot. The wiper sweeps through an angle of $110^\circ$. The blade extends from $10$ cm to $50$ cm from the pivot.
- a) Find the area of the region swept by the blade, correct to the nearest cm$^2$.
- b) Find the distance travelled by the tip of the blade (the point $50$ cm from the pivot) in one sweep, correct to the nearest cm.
A sector of a circle has a radius of $12$ cm and an area of $48\pi$ cm$^2$. a) Find the central angle of the sector. b) Find the length of the arc, in terms of $\pi$. c)…
A sector of a circle has a radius of $12$ cm and an area of $48\pi$ cm$^2$.
- a) Find the central angle of the sector.
- b) Find the length of the arc, in terms of $\pi$.
- c) Find the perimeter of the sector, correct to one decimal place.
A sector of a circle has a perimeter of $30$ cm and a radius of $8$ cm. a) Find the arc length. b) Find the central angle, correct to the nearest degree. c) Find the…
A sector of a circle has a perimeter of $30$ cm and a radius of $8$ cm.
- a) Find the arc length.
- b) Find the central angle, correct to the nearest degree.
- c) Find the area of the sector, correct to one decimal place.
A circle with centre $O$ has radius $10$ cm. Points $A$ and $B$ lie on the circle and $\angle AOB = 80^\circ$. a) Find the area of the sector $AOB$, correct to one…
A circle with centre $O$ has radius $10$ cm. Points $A$ and $B$ lie on the circle and $\angle AOB = 80^\circ$.
- a) Find the area of the sector $AOB$, correct to one decimal place.
- b) Find the area of triangle $AOB$, correct to one decimal place.
- c) Hence find the area of the segment between the chord $AB$ and the arc $AB$.
A sector of radius $r$ cm has central angle $\theta^\circ$. The arc length is equal to the radius. a) Show that $\theta = \dfrac{180}{\pi}$. b) Hence show that the area…
A sector of radius $r$ cm has central angle $\theta^\circ$. The arc length is equal to the radius.
- a) Show that $\theta = \dfrac{180}{\pi}$.
- b) Hence show that the area of the sector is $\dfrac{r^2}{2}$.
- c) Find $r$ if the area of the sector is $50$ cm$^2$.