document.write( "Question 1146043: The volume of a sphere is increased by 72.8%. What is the percentage increase in the radius? \n" ); document.write( "

Algebra.Com's Answer #767320 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The volume of a sphere is proportional to the cube of the radius.

\n" ); document.write( "An increase of 72.8% in the volume means the ratio of the new and old volumes is

\n" ); document.write( " $\"%28100%2B72.8%29%2F100+=+172.8%2F100+=+1728%2F1000\"$

\n" ); document.write( "The ratio of the volumes is the cube of the ratio of the radii, so the ratio of the radii is the cube root of the ratio of the volumes:

\n" ); document.write( " $\"%281728%2F1000%29%5E%281%2F3%29+=+12%2F10+=+1.20\"$

\n" ); document.write( "So the percent increase in the radius is 20%. \n" ); document.write( "

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