SOLUTION: The slant height of a cone is doubled. Does this double the surface area of the cone? Explain your reasoning.

Algebra ->  Surface-area -> SOLUTION: The slant height of a cone is doubled. Does this double the surface area of the cone? Explain your reasoning.      Log On


   

Question 1172878: The slant height of a cone is doubled. Does this double the surface area of the cone? Explain your
reasoning.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The lateral surface area of a cone is %28pi%29%28r%29%28l%29, where r is the radius of the base and l is the slant height.

The area of the base is %28pi%29%28r%5E2%29.

The intent of the question is not clear....

(1) If only the slant height of the cone is doubled (the radius of the cone is unchanged), then the LATERAL surface area is doubled. The (total) surface area of the cone -- which is literally what the question asks for, is NOT doubled, because the surface area of the base does not change.

(2) If the "new" cone is similar to the original -- which means the slant height and radius are both doubled, then we have two similar solids with scale factor 2; the ratio of surface areas is 4:1. So in this case the surface area is multiplied by a factor of 4, not 2.

ANSWER: Yes, the surface area is doubled -- IF only the slant height is doubled AND by "surface area" you are only talking about LATERAL surface area.