Question

the radius of a circle is 6cm and the area of the sector of this circle is
$18 \times \frac{6}{7}$

${cm}^{2}$
what is the angle of the sector
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Answer 1

$\huge\color{orange}\boxed{\colorbox{black}{\tt{☣ANSWER☣}}}$

★Step 1 : Calculate the area of the circle

$\implies\pi {r}^{2}$

$\implies \frac{22}{7} \times {6}^{2}$

$\implies \frac{22}{7} \times 36$

$\implies113.14 \: c {m}^{2}$

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★Step 2 : Find the percentage of the area of sector upon the area of the circle

$( 18 \times \frac{6}{7} ) \div 113.14 \times 100$

$\implies13.63 \: percent$

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★Step 3 : Calculate the angle of the sector

• Total angle of the circle = 360°
• Percentage of the sector's angle = 13.63%
• Angle of the sector :
• $\frac{13.63}{100} \times 360$
• $\implies49 \degree$