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