Question 117074
Wow! That's a pretty big sphere. A diameter of 20 km is equivalent to a diameter of almost 12.5 miles!
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Anyhow, the formula for the volume (V) of a sphere is:
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{{{V = (4/3)*pi*r^3}}}
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where V is the volume and r is the radius of the sphere.
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If the diameter of a sphere is 20 km, then the radius of that sphere is half that or the radius
of the given sphere is 10 km.
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Substituting 10 km for r in the volume equation results in:
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{{{V = (4/3)*pi*10^3}}}
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and {{{10^3 = 10 * 10*10 = 1000}}}
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This says that we can substitute 1000 for {{{r^3}}} in the formula to get:
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{{{V = (4/3)*pi*1000}}}
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Multiplying the 1000 times the {{{(4/3)}}} results in {{{(4000/3)}}} and dividing the
4000 by 3 results in {{{1333.33333333}}}. Substituting 1333.33333333 for {{{(4/3)*1000}}}
reduces the equation to:
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{{{V = (1333.33333333)*pi}}}
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and using a scientific calculator we can multiply out 1333.33333333 times {{{pi}}} to get:
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{{{V = 4188.790205}}}
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And since the radius was in kilometers this answer is in cubic kilometers. So the answer to
this problem is:
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Volume = 4188.790205 cubic kilometers
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Hope this helps you to understand the problem a little better.
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