document.write( "Question 6771: In 1974, the French Army sent soldiers up in hot air balloons to observe enemy troop movements. One such balloon, L'Entrepenant, had a volume of 256 (pi)/3.\r
\n" ); document.write( "\n" ); document.write( "a)Solve the formula for the volume of a sphere (V=4/3 (pi)r (cubed) for r cubed. Then use this formula to calculate the radius of the L'Entrepenant balloon.\r
\n" ); document.write( "\n" ); document.write( "b) What was the diameter of the L'Entrepenant balloon?\r
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\n" ); document.write( "\n" ); document.write( "UGH!\r
\n" ); document.write( "\n" ); document.write( "i appreciate your time- this is my step-daughter's homework problem and it has us both baffled! \n" ); document.write( "
Algebra.Com's Answer #3731 by ichudov(507)\"\" \"About 
You can put this solution on YOUR website!
This is a problem of mostly translating English to algebrese. \r
\n" ); document.write( "\n" ); document.write( "What they say is that volume is \"256%2Api%2F3\". \r
\n" ); document.write( "\n" ); document.write( "They also mention that the volume of a sphere is \"4%2F3%2Api%2Ar%5E3\".\r
\n" ); document.write( "\n" ); document.write( "So, we have \"256%2Api%2F3+=+4%2F3%2Api%2Ar%5E3\".\r
\n" ); document.write( "\n" ); document.write( "Remove pi:\r
\n" ); document.write( "\n" ); document.write( "\"256%2F3=4%2F3%2Ar%5E3\"\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "


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  • This is an equation! Solutions: r=4.
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  • Graphical form: \"256%2F3=4%2F3%2Ar%5E3\" simplifies to \"%2B-1.33333333333333%2Ar%5E2-5.33333333333333%2Ar-21.3333333333333=0\"
  • Text form: 256/3=4/3*r^3 simplifies to +-1.33333333333333*r^2-5.33333333333333*r-21.3333333333333=0
  • Cartoon (animation) form: \"simplify_cartoon%28+256%2F3=4%2F3%2Ar%5E3+%29\"
    For tutors: simplify_cartoon( 256/3=4/3*r^3 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"256%2F3=highlight_red%28+4%2F3%2Ar%5E3+%29\".
Moved these terms to the left \"highlight_green%28+-4%2F3%2Ar%5E3+%29\"
It becomes \"256%2F3-highlight_green%28+4%2F3%2Ar%5E3+%29=0\".
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Look at \"highlight_red%28+256%2F3+%29-4%2F3%2Ar%5E3=0\".
Moved \"256%2F3\" to the right of expression
It becomes \"-4%2F3%2Ar%5E3%2Bhighlight_green%28+256%2F3+%29=0\".
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Look at \"highlight_red%28+-4%2F3%2Ar%5E3%2B256%2F3+%29=0\".
Divided polynomial on the left by known factors (r-(4))
It becomes \"%2Bhighlight_green%28+-1.33333333333333%2Ar%5E2-5.33333333333333%2Ar-21.3333333333333+%29=0\".
Result: \"%2B-1.33333333333333%2Ar%5E2-5.33333333333333%2Ar-21.3333333333333=0\"
\n" ); document.write( "This is an equation! Solutions: r=4.

Universal Simplifier and Solver

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Done!
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\n" ); document.write( "\n" ); document.write( "So, the radius is 4, and the diameter is twice more, or 8. \n" ); document.write( "
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