Originally posted by: Kyteland
I don't know if there is a way to isolate the radius, because the slant is a function of the radius.
The area of a cone is pi*r^2 + pi*r*sqrt(r^2+h^2)
If you triple the radius you end up with 9*pi*r^2 + 3*pi*r*sqrt(9*r^2+h^2)
You can't reduce that ratio much
pi*r^2 + pi*r*sqrt(r^2+h^2) : 9*pi*r^2 + 3*pi*r*sqrt(9*r^2+h^2)
r^2 + r*sqrt(r^2+h^2) : 9*r^2 + 3*r*sqrt(9*r^2+h^2) // remove a factor of pi
r + sqrt(r^2+h^2) : 9*r + 3*sqrt(9*r^2+h^2) // remove a factor of r
That's about the best you can do unless you have more information.
The slant value is a function of both the height and the radius. In a cone there are only two surfaces. The surface area is determined by adding the two together. The base is easy, it's just a circle with radius r. That's the pi*r^2 term.Originally posted by: zerocool1
how is slant a factor of the radius? assuming a right triangle nothing else matters. ceteris paribus...