Circular measure: แบบฝึกหัด

A sector of a circle has a radius of \(8\) cm and a central angle of \(1.5\) radians. Find the perimeter of the sector.

Find the area of a sector of a circle with radius \(6\) cm and an arc length of \(\pi\) cm.

A sector of a circle has a radius of \(r\) cm and an area of \(50\) cm\(^2\). If the perimeter of the sector is \(30\) cm, find the two possible values of \(r\).

The area of a sector of a circle is \(20\) cm\(^2\) and the radius of the circle is \(5\) cm. Find the perimeter of the sector.

A sector of a circle has a radius of \( 15 \) cm and an angle of \( 0.8 \) radians at the centre.
(a) Find the length of the arc of the sector.
(b) Find the perimeter of the sector.
(c) Find the area of the sector.

In the diagram, a circle with centre \( O \) and radius \( 10 \) cm contains a chord \( AB \) of length \( 12 \) cm.
(a) Show that the angle \( AOB \) is approximately \( 1.287 \) radians.
(b) Calculate the area of the minor segment bounded by the chord \( AB \) and the arc \( AB \).