document.write( "Question 412210: Find the area of the sector formed by central angle θ = 3π/5 in a circle of radius r = 8 m. (Round the answer to two decimal places.) \n" ); document.write( "

Algebra.Com's Answer #289667 by jsmallt9(3758) $\"\"$ $\"About$

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Central angles, their arcs and the areas of the sectors formed are all proportional:
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document.write( "     central angle           arc length           area of sector\r\n" );
document.write( "  ------------------    =   -------------   =   ------------------\r\n" );
document.write( "  2pi or 360 degrees        Circumference       area of the circle\r\n" );
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\n" ); document.write( "For your problem, which references central angles and area of a sector, we will use the first and third fractions:
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document.write( "     central angle            area of sector\r\n" );
document.write( "  ------------------    =   ------------------\r\n" );
document.write( "  2pi or 360 degrees        area of the circle\r\n" );
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\n" ); document.write( "Since your central angle is expressed in radians we will use $\"2pi\"$ in the denominator of the first fraction:
\n" ); document.write( " $\"%283pi%2F5%29%2F2pi+=+x%2F%28pi%2A8%5E2%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"3%2F10+=+x%2F64pi\"$
\n" ); document.write( "Cross multiplying we get:
\n" ); document.write( " $\"192pi+=+10x\"$
\n" ); document.write( "Dividing by 10 we get:
\n" ); document.write( " $\"192pi%2F10+=+x\"$
\n" ); document.write( "All that's left is to replace $\"pi\"$ with a decimal (3.14159....), simplify the fraction and round off the answer. I'll leave that up to you. \n" ); document.write( "

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