document.write( "Question 1105414: If you triple the radius of a cone and change the slant height so that it is one-third of what it was before, by how much will the total area of the cone increase? \n" ); document.write( "

Algebra.Com's Answer #720235 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The total surface area of a cone is the lateral surface area plus the area of the base:
\n" ); document.write( " $\"A+=+%28pi%29%28r%29%28l%29+%2B+%28pi%29%28r%5E2%29\"$

\n" ); document.write( "If the radius of the cone is tripled and the slant height is cut by a factor of 3, the lateral surface area stays the same:
\n" ); document.write( " $\"%28pi%29%283r%29%28l%2F3%29+=+%28pi%29%28r%29%28l%29\"$

\n" ); document.write( "The area of the base changes; it is now
\n" ); document.write( " $\"%28pi%29%283r%29%5E2+=+9%28pi%29%28r%5E2%29\"$

\n" ); document.write( "The lateral surface area stays the same; the area of the base increases by $\"8%28pi%29%28r%5E2%29\"$ ; so the total surface area of the cone increases by $\"8%28pi%29%28r%5E2%29\"$ . \n" ); document.write( "

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