SOLUTION: Two solid cones are mathematically similar. Cone X has a volume of 120cm^3. Cone Y has a volume of 960cm^3. Work out the ratio of the surface area of cone X to the surface ar

Algebra ->  Surface-area -> SOLUTION: Two solid cones are mathematically similar. Cone X has a volume of 120cm^3. Cone Y has a volume of 960cm^3. Work out the ratio of the surface area of cone X to the surface ar      Log On


   



Question 1076993: Two solid cones are mathematically similar.
Cone X has a volume of 120cm^3.
Cone Y has a volume of 960cm^3.
Work out the ratio of the surface area of cone X to the surface area of cone Y.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The surface area of a cone is of the form pi*r(r+sqrt (h^2+r^2)). This is proportional to the second power of r.
The volume ratio is 1:8, and volume is to the third power.
This is equivalent of one cone's radius being 1 and the other's being 2. When one cubes both to compute volume, there is a 1:8 ratio.
The area, however, is to the second power and will be 1:4.