Circles, arcs and sectors: แบบฝึกหัด

In the diagram, a sector of a circle with radius 9 cm has a sector angle of \(40^\circ\). Calculate the area of the sector in terms of \(\pi\).

In the diagram, a shape is formed by a rectangle \(ABCD\) and a semi-circle with diameter \(AD\). The length \(AB = 10\text{ cm}\) and the length \(BC = 6\text{ cm}\). The semi-circle is attached to the outside of the rectangle along side \(AD\). Calculate the total area of the shape, giving your answer in terms of \(\pi\).

An arc of a circle with a radius of 15 cm subtends an angle of \(120^\circ\) at the center of the circle. Calculate the length of this arc in terms of \(\pi\).

A sector of a circle has an area of \(24\pi\) cm\(^2\) and a radius of 8 cm. Calculate the perimeter of this sector in terms of \(\pi\).

A circle has an area of \(36\pi \text{ cm}^2\). Calculate the perimeter of a semi-circle with the same radius, leaving your answer in terms of \(\pi\).

A garden path is in the shape of a sector of a circle with a radius of 15 m. The angle at the center of the sector is \(72^\circ\).

(a) Show that the area of the path is \(45\pi\text{ m}^2\).
(b) The path is to be paved with stones. One bag of stones covers an area of \(5\text{ m}^2\). Using \(\pi = 3.142\), calculate the minimum number of bags required to cover the path.
(c) Calculate the total perimeter of the path. Give your answer correct to 1 decimal place.