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?

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) (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:

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:

The area of the base changes; it is now

The lateral surface area stays the same; the area of the base increases by ; so the total surface area of the cone increases by .
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