The diagram shows a sector ORST of a circle with centre O. OR = OT = 10.4 cm. Angle ROT = 120°. (a) Calculate the length of the arc RST of the sector (3s.f)
Before using a more complex formula it is better to know how to answer the question using a simpler method.
From the diagram we can see that this is a sector from a circle. We need to find out the area of the shaded segment which we can see will be:
Area of the sector - area of the triangle = area of the segment
The area of the sector is found by working out what proportion of the circle the sector is using the centre O angle of 120 degrees. We know that the centre of a circle is 360 degrees because it is a full rotation. Therefore we 120/360 = 1/3 (This sector is a third of the circle)
Since the area of a circle = pie x radius2
We substitute in our own numbers to find the area of the whole circle = pie x 10.4cm2
= 2704/25 pie
Further to this we divide it by 3
=2704/75 pie
The area of a triangle can be calculated using: 1/2 x a x b x sin(C). In this case a would be OR and a would be OT and C is the angle O.
= 0.5 x 10.4 x 10.4 x sin(120) = 46.83465384cm2
The final answer is calculated with one short subtraction
2704/75 pie - 46.83465384 = 66.430233cm2
= 66.4cm2 (3s.f)
REMEMBER TO ROUND TO THE INDICATED SIGNIFICANT FIGURES AND USE THE CORRECT UNITS
