SOLUTION: 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?

Algebra ->  Surface-area -> SOLUTION: 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?      Log On


   

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?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The total surface area of a cone is the lateral surface area plus the area of the base:
A+=+%28pi%29%28r%29%28l%29+%2B+%28pi%29%28r%5E2%29

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:
%28pi%29%283r%29%28l%2F3%29+=+%28pi%29%28r%29%28l%29

The area of the base changes; it is now
%28pi%29%283r%29%5E2+=+9%28pi%29%28r%5E2%29

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.