Circles, arcs and sectors：練習問題

A semicircle has a diameter of 14 cm. Calculate the total perimeter of the semicircle. Use \( \pi = \frac{22}{7} \).

A sector of a circle has a central angle of \( 60^\circ \) and an arc length of \( 6\pi \) cm. Find the radius of the circle.

The area of a sector is \(12\pi \text{ cm}^2\). If the angle of the sector is \(108^\circ\), find the radius of the sector.

A circle has a diameter of \(12\) cm. Calculate its area, giving your answer in terms of \(\pi\).

In a circle with centre \(O\) and radius \(9\) cm, a sector has a central angle of \(120^\circ\). Calculate the length of the arc of this sector, giving your answer in terms of \(\pi\).

A semicircle has a radius of 4 cm. Calculate its area, giving your answer in terms of \( \pi \).

A circle has a radius of \(r\) cm. If the area of the circle is numerically equal to its circumference, calculate the value of \(r\).

A sector of a circle has a radius of \(10 \text{ cm}\) and an angle of \(108^\circ\). Calculate the perimeter of the sector. Give your answer correct to 3 significant figures.

A circle has a radius of 12 cm. A sector of this circle has a central angle of \( 60^\circ \).

(a) Calculate the circumference of the circle, giving your answer in terms of \( \pi \).

(b) Calculate the area of the circle, giving your answer in terms of \( \pi \).

(c) Calculate the arc length of the sector, giving your answer in terms of \( \pi \).

(d) Calculate the area of the sector, giving your answer in terms of \( \pi \).

The diagram shows a circle with centre \(O\) and radius \(10 \text{ cm}\). A chord \(AB\) is \(12 \text{ cm}\) long.
(a) Calculate the perpendicular distance from the centre \(O\) to the chord \(AB\).

(b) Calculate the angle \(AOB\) in degrees. Give your answer correct to one decimal place.

(c) Calculate the area of the minor segment cut off by the chord \(AB\). Give your answer correct to 3 significant figures.