How does the surface area of the new cone compare to the surface area of the original cone?

Question

You cut away part of a right cone with a radius of 6 inches and a slant height of 12 inches to form a smaller right cone with a radius of 3 inches and a slant height of 6 inches.

The surface area of the new cone is ___ times the surface area of the original cone.

Answer 1

To find the scale factor, k, take the ratio of corresponding parts of the new triangle over the original triangle:

(new slant height)/(original slant height) = 6/12 = 1/2

(new radius)/(original radius) = 3/6 = 1/2

So k = 1/2. The ratio of the surface areas is:

(new surface area)/(original surface area) = k² = (1/2)² = ____?