Your Practice Set – Applications and Interpretation for IBDP Mathematics
16
Paper 1 – Areas and Perimeters of Sectors
Example
The following diagram shows a circle with centre O and radius 35 cm .
The points A , B and C are on the circumference of the circle and AOC ˆ � 0.82 rad .
( a ) ( i ) Find the length of arc ABC .
( ii ) Hence , find the perimeter of sector OABC .
( b ) Find the exact area of sector OABC .
[ 4 ]
[ 2 ]
Solution
( a ) ( i ) The length of arc ABC � ( 35 )( 0.82 )
( A1 ) for substitution
� 28.7 cm A1
( ii ) |
The perimeter of sector OABC |
|
� 28.7 �35 �
35
|
( M1 ) for valid approach |
|
�
98.7 cm
|
A1 |
( b ) The area of sector OABC 1 ( 35 )
2 � ( 0 . 82 )
( A1 ) for substitution 2
2
� 502.25 cm A1
[ 4 ]
[ 2 ]
46
SE Production Limited