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

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) (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 .
They also mention that the volume of a sphere is .
So, we have .
Remove pi:

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

YOUR ANSWER

This is an equation! Solutions: r=4.
Graphical form: simplifies to
Text form: 256/3=4/3*r^3 simplifies to +-1.33333333333333*r^2-5.33333333333333*r-21.3333333333333=0
Cartoon (animation) form:
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 .
Moved these terms to the left highlight_green%28+-4%2F3%2Ar%5E3+%29

It becomes .

Look at .
Moved 256%2F3

to the right of expression
It becomes .

Look at .
Divided polynomial on the left by known factors (r-(4))
It becomes .
Result:
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.
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