Chapter 23

Find the circumference of a circle of radius \(12.0 \mathrm{~cm}\).

If the diameter of a circle is \(75 \mathrm{~mm}\), find its circumference.

Determine the radius of a circle if its perimeter is \(112 \mathrm{~cm}\).

Convert to radians: (a) \(125^{\circ}\) (b) \(69^{\circ} 47^{\prime}\)

Convert to degrees and minutes: (a) \(0.749\) radians (b) \(3 \pi / 4\) radians

Express in radians, in terms of \(\pi\) (a) \(150^{\circ}\) (b) \(270^{\circ}\) (c) \(37.5^{\circ}\)

Find the length of arc of a circle of radius \(5.5 \mathrm{~cm}\) when the angle subtended at the centre is \(1.20\) radians.

Determine the diameter and circumference of a circle if an arc of length \(4.75 \mathrm{~cm}\) subtends an angle of \(0.91\) radians.

If an angle of \(125^{\circ}\) is subtended by an arc of a circle of radius \(8.4 \mathrm{~cm}\), find the length of (a) the minor arc, and (b) the major arc, correct to 3 significant figures.

Determine the angle, in degrees and minutes, subtended at the centre of a circle of diameter \(42 \mathrm{~mm}\) by an arc of length \(36 \mathrm{~mm}\). Calculate also the area of the minor sector formed.

A football stadium floodlight can spread its illumination over an angle of \(45^{\circ}\) to a distance of \(55 \mathrm{~m}\). Determine the maximum area that is floodlit.

An automatic garden spray produces a spray to a distance of \(1.8 \mathrm{~m}\) and revolves through an angle \(\alpha\) which may be varied. If the desired spray catchment area is to be \(2.5 \mathrm{~m}^{2}\), to what should angle \(\alpha\) be set, correct to the nearest degree.

Determine (a) the radius, and (b) the co-ordinates of the centre of the circle given by the equation: $$ x^{2}+y^{2}+8 x-2 y+8=0 $$

Sketch the circle given by the equation: $$ x^{2}+y^{2}-4 x+6 y-3=0 $$