SOLUTION: 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. a)Solve the formula

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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.
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.
b) What was the diameter of the L'Entrepenant balloon?

UGH!
i appreciate your time- this is my step-daughter's homework problem and it has us both baffled!
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
This is a problem of mostly translating English to algebrese.
What they say is that volume is 256%2Api%2F3.
They also mention that the volume of a sphere is 4%2F3%2Api%2Ar%5E3.
So, we have 256%2Api%2F3+=+4%2F3%2Api%2Ar%5E3.
Remove pi:
256%2F3=4%2F3%2Ar%5E3
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: r=4.
  • 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 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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.
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
This is an equation! Solutions: r=4.

Universal Simplifier and Solver


Done!
.
So, the radius is 4, and the diameter is twice more, or 8.