-Where is the degree measure for the arc of a sector of a circle, the ratio of the area of the sector to that of the area of the circle is given by . Use this ratio to explain why
the area of the sector is given by .
[Note: In the figure, the sector with arc measure is bounded by radii , , and .]

Question

-Where  is the degree measure for the arc of a sector of a circle, the ratio of the area of the sector to that of the area of the circle is given by  . Use this ratio to explain why
the area of the sector is given by  .
[Note: In the figure, the sector with arc measure  is bounded by radii  ,  , and  .]

Quizplus · Accepted Answer

The Answer is Given that Given that , it follows that . Where r is the length of radius of the circle, the area of the circle is given by . By substitution, it follows that .

Given that , it follows that . Where r is the length of radius of the circle, the area of the circle is given by . By substitution, it follows that .

, it follows that Given that , it follows that . Where r is the length of radius of the circle, the area of the circle is given by . By substitution, it follows that .

. Where r is the length of radius of the circle, the area of the circle is given by Given that , it follows that . Where r is the length of radius of the circle, the area of the circle is given by . By substitution, it follows that .

. By substitution, it follows that Given that , it follows that . Where r is the length of radius of the circle, the area of the circle is given by . By substitution, it follows that .

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-Where Is the Degree Measure for the Arc of a Sector