document.write( "Question 103758: The surface area of a sphere varies directly with the square of its radius. If the surface area of a sphere with a radius of 12 inches if 576 square inches, find the surface area of a sphere with a radius of 3 inches \n" ); document.write( "

Algebra.Com's Answer #75409 by Earlsdon(6294) $\"\"$ $\"About$

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From the problem you can write:
\n" ); document.write( " $\"S+=+kr%5E2\"$ Where S = surface area and k = the proportionality constant.
\n" ); document.write( "If S = 576 when r = 12, then we can find the value of k.
\n" ); document.write( " $\"576+=+k%2812%29%5E2\"$
\n" ); document.write( " $\"576+=+9%28144%29\"$ Divide both sides by 144.
\n" ); document.write( " $\"576%2F144+=+k\"$
\n" ); document.write( " $\"k+=+4\"$ so...
\n" ); document.write( " $\"S+=+4r%5E2\"$
\n" ); document.write( "Now, when r = 3 you can find S.
\n" ); document.write( " $\"S+=+4%283%29%5E2\"$
\n" ); document.write( " $\"S+=+4%289%29\"$
\n" ); document.write( " $\"S+=+36\"$ sq.in.
\n" ); document.write( "In reality, the surface area of a sphere is given by:
\n" ); document.write( " $\"S+=+4%28pi%29r%5E2\"$ so the surface area of a shere whose radius is 12 in. would be:
\n" ); document.write( " $\"S+=+4%28pi%29%2812%29%5E2\"$
\n" ); document.write( " $\"S+=+4%28pi%29%28144%29\"$
\n" ); document.write( " $\"S+=+576%28pi%29\"$ sq.in.
\n" ); document.write( "And, if the radius of the sphere is 3 in.. then:
\n" ); document.write( " $\"S+=+4%28pi%29%283%29%5E2\"$
\n" ); document.write( " $\"S+=+4%28pi%29%289%29\"$
\n" ); document.write( " $\"S+=+36%28pi%29\"$ sq.in. \n" ); document.write( "

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