Question

For a cone, if the radius was quadrupled and the slant height was reduced to 1/6 of its original size what would be the formula to find the modified surface area.

Answer 1

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
`\frac16`, then the new area is


`A=\pi(4r)^2+\pi (4r)\left(\frac\ell6\right)`

`A=16\pi r^2+\frac23\pi r\ell`