91Ó°ÊÓ

Find the area of a circular metal plate, correct to the nearest square millimetre, having a diameter of \(35.0 \mathrm{~mm}\).

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

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.

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.

A wheel of diameter \(540 \mathrm{~mm}\) is rotating at \(\frac{1500}{\pi}\) rev/min. Calculate the angular velocity of the wheel and the linear velocity of a point on the rim of the wheel.

A car is travelling at \(64.8 \mathrm{~km} / \mathrm{h}\) and has wheels of diameter \(600 \mathrm{~mm}\). (a) Find the angular velocity of the wheels in both \(\mathrm{rad} / \mathrm{s}\) and rev/min. (b) If the speed remains constant for \(1.44 \mathrm{~km}\), determine the number of revolutions made by the wheel, assuming no slipping occurs.