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Mathematics

Grade9

Easy

Question

A plot of land is in the shape of a sector of a circle of radius 28 m. If the sectorial angle (central angle) is 60°, find the area and the perimeter of the plot.

Area = 512.7; perimeter = 65.43
Area = 410.7; perimeter = 85.33
Area = 456.1; perimeter = 54.33
Area = 643.1; perimeter = 86.33

hint Hint:

$A equals pi r to the power of 2 end exponent$
Circumference = 2× $pi$ ×r
Area of the sector $equals fraction numerator A n g l e o f sec invisible function application t o r over denominator 360 to the power of 0 end exponent end fraction cross times pi r to the power of 2 end exponent$

The correct answer is: Area = 410.7; perimeter = 85.33

Area of the plot= $fraction numerator 60 to the power of ring operator end exponent over denominator 360 to the power of ring operator end exponent end fraction cross times pi to the power of 2 end exponent$ [Since $theta equals 60$ ]
$equals fraction numerator 1 over denominator 6 end fraction cross times pi r to the power of 2 end exponent$
$equals fraction numerator 1 over denominator 6 end fraction cross times fraction numerator 22 over denominator 7 end fraction cross times 28 to the power of 2 end exponent text end text m to the power of 2 end exponent$
$equals fraction numerator 1 over denominator 6 end fraction cross times fraction numerator 22 over denominator 7 end fraction cross times 784 text end text m to the power of 2 end exponent$
$equals fraction numerator 17248 over denominator 42 end fraction text end text m to the power of 2 end exponent$
$equals fraction numerator 1232 over denominator 3 end fraction text end text m to the power of 2 end exponent$
$equals 410 fraction numerator 2 over denominator 3 end fraction text end text m to the power of 2 end exponent$
Perimeter of the plot = $open parentheses fraction numerator pi theta over denominator 180 end fraction plus 2 close parentheses r$
$equals open parentheses fraction numerator 22 over denominator 7 end fraction cross times fraction numerator 60 over denominator 180 end fraction plus 2 close parentheses 28 text end text m$
$equals open parentheses fraction numerator 22 over denominator 21 end fraction plus 2 close parentheses 28 text end text m$
$equals fraction numerator 64 over denominator 21 end fraction cross times 28 text end text m$
$equals fraction numerator 1792 over denominator 21 end fraction text end text m$
$equals fraction numerator 256 over denominator 3 end fraction text end text m$
$equals 85 fraction numerator 1 over denominator 3 end fraction text end text m$

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