document.write( "Question 1089416: In a figure, the circle has center O and radius 3. If the area of the minor sector AB is between 5 and 10. What's one possible integer value of arc length s that's in middle of AB? \n" ); document.write( "

Algebra.Com's Answer #703809 by KMST(5328) $\"\"$ $\"About$

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I understand that the sector and circle look like the drawing below,
\n" ); document.write( "and that the problem asks for one possible integer value for the length of the arc shown in red.
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\n" ); document.write( "The area of a sector or a circle with radius $\"R\"$
\n" ); document.write( "and length of arc or circumference $\"L\"$ is
\n" ); document.write( " $\"area=R%2AL%2F2\"$ .
\n" ); document.write( "(If that reminds you of the formula for area of a triangle, it is not a coincidence).
\n" ); document.write( "In this case, we are told that for the sector with arc length $\"AB=L\"$
\n" ); document.write( " $\"5%3C3L%2F2%3C10\"$ .
\n" ); document.write( "Multiplying all three sides of that inequality times $\"2%2F3\"$ , we get
\n" ); document.write( " $\"5%282%2F3%29%3CL%3C10%282%2F3%29\"$
\n" ); document.write( " $\"10%2F3%3CL%3C20%2F3\"$
\n" ); document.write( " $\"3%261%2F3%3CL%3C6%262%2F3\"$ .
\n" ); document.write( "So, possible integer arc lengths are $\"L=4\"$ or $\"L=5\"$ or $\"L=6\"$ .
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