Let \(r\) be the radius of the cone's base and \(\ell\) the slant height.
The surface area of a cone is
\(A=\pi r^2+\pi r\ell\)
If the radius is quadrupled (\(r\to4r\)) and the slant height scaled by a factor of \(\dfrac16\), then the new area is
\(A=\pi(4r)^2+\pi (4r)\left(\dfrac\ell6\right)\)
\(A=16\pi r^2+\dfrac23\pi r\ell\)
