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Mathematics

Grade9

Easy

Question

Find the area of the sector and also find the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm.

Area = 693 square cm; Angle = 180 degrees
Area = 705 square cm; Angle = 185 degrees
Area = 540 square cm; Angle = 164 degrees
Area = 800 square cm; Angle = 210 degrees

hint Hint:

we have to remember this two formula below given
area of sector = $fraction numerator r a d i u s space cross times space a r c space l e n g t h over denominator 2 end fraction equals fraction numerator l r over denominator 2 end fraction$

The correct answer is: Area = 693 square cm; Angle = 180 degrees

( option 1) is the correct answer
Area of the sector $equals fraction numerator I r over denominator 2 end fraction$
Substitute r=21 and I=66.
$equals fraction numerator 66 cross times 21 over denominator 2 end fraction$
$equals 693 text end text c m to the power of 2 end exponent$
Using the area of the sector $693 text end text c m to the power of 2 end exponent$ , find the central angle $theta$ .
Area of the sector $equals 693 text end text c m to the power of 2 end exponent$
$fraction numerator theta over denominator 360 to the power of ring operator end exponent end fraction cross times pi r to the power of 2 end exponent equals 693$
Substitute $r equals 21$ and $pi almost equal to fraction numerator 22 over denominator 7 end fraction$
$left parenthesis fraction numerator theta over denominator 360 to the power of ring operator end exponent end fraction right parenthesis cross times left parenthesis fraction numerator 22 over denominator 7 end fraction right parenthesis cross times 21 to the power of 2 end exponent equals 693$
$open parentheses fraction numerator theta over denominator 60 to the power of ring operator end exponent end fraction close parentheses cross times 231 equals 693$
$theta equals 693 cross times open parentheses fraction numerator 60 to the power of ring operator end exponent over denominator 231 end fraction close parentheses$
$theta equals 180 to the power of ring operator end exponent$

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