maths Trigonometry

Question

A car windscreen wiper traces out the area ABCD, where AB and CD are arcs of circles with centre O and radii 60cm and 30cm respectively. Angle AOB measures 120.

a) Find the area of ABCD in exact form

b) Find the perimeter of ABCD in exact form

Answer 1

Revolving each wiper 360° makes concentric circles with radii 60 and 30cm.

Let Ο be a circle nomenclature.

ΟAB = Πr₁² = Π60²

ΟCD = Πr₂² = Π30²

Taking the arc length of 120°, this is 1/3 of a circles area.

The difference is Π60² - Π30² = 2700Π

So 1/3 of this is the area ABCD = 900Π = 2827 cm²

Perform the same logic using the circumference of each circle and 1/3 of that, with the length of the radii,

to get the perimeter of ABCD