Question 218249
A sphere has surface area of 1296 pi in^2. find the volume of the sphere.
The choices are


A)24 pi in^3 B)1944 pi in^3
C)432 pi in^3 D)7776 pi in^3


Step 1.  The surface area  S of a sphere is given as {{{S=4*pi*r^2}}}.  So


{{{S=1296=4*pi*r^2}}}


Divide {{{4*pi}}} to both sides of the equation


{{{1296/(4*pi)=r^2}}}


Take the square root to both sides of the equation


{{{sqrt(1296/(4*pi))=r}}}


Step 2.  The volume V of a sphere is given as {{{V=4/3*pi*r^3}}}.  then


{{{V=4/3*pi*r^3}}}


{{{V=4/3*pi*(sqrt(1296/(4*pi)))^3}}}


{{{V=4/3*pi*(1296/(4*pi))^(3/2)}}}  where {{{sqrt(x)=x^(1/2)}}} or {{{(sqrt(x))^3=x^(3/2)}}}


{{{V=1/(3*sqrt(4*pi))*1296^(3/2)}}}  where I cancelled the {{{4*pi}}} in numerator leaving {{{sqrt(4*pi)}}} in denominator


{{{V=1296^(3/2)*sqrt(pi)/(3*2*pi)}}}  where I multiplied by {{{sqrt(pi)/sqrt(pi)=1}}} to get rid of square root of pi in denominator.


{{{V=1296^(3/2)*sqrt(pi)/(6*pi)}}}


{{{V=1296^(3/2)*sqrt(pi)/(6*pi)}}}


{{{V=7776*sqrt(pi)/pi}}}


Step 3.  ANSWER is {{{V=7776*sqrt(pi)/pi}}}.  I don't see this answer among your choices.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J


drjctu@gmail.com


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