Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#2

Hits: 182

Question

In the diagram, OAB and OCD are radii of a circle, centre O and radius 16 cm. Angle radians. AC and BD are arcs of circles, centre O and radii 10 cm and 16 cm respectively.


i.       
In the case where , find the area of the shaded region.

   ii.       Find the value of  for which the perimeter of the shaded region is 28.9 cm.

Solution

From the given information we can compile following data;

     i.
 

From the given diagram it is evident that;

Expression for area of a circular sector with radius  and angle  rad is;

Therefore;

For ;

   ii.
 

From the given diagram it is evident that;

We know that;

Expression for length of a circular arc with radius  and angle  rad is;

Therefore;

Please follow and like us:
0

Comments