Answer:
A.
[tex] SA= \frac{2}{3} \pi rl+16 \pi r^2[/tex]
Step-by-step explanation:
Surface area of the original cone
[tex] SA= \pi r l + \pi r^2... (1)[/tex]
When, radius is quadrupled and slant height is reduced to one sixth
[tex] i. e. \: \:r = 4r\: \: \&\:\: l= \frac{1}{6}l[/tex]
Plug the above values of r and [tex] l[/tex] in equation (1), new surface area becomes:
[tex] SA= \pi (4r)\times \frac{1}{6} l+ \pi (4r)^2[/tex]
[tex] SA= \frac{4}{6} \pi rl+16 \pi r^2[/tex]
[tex]\huge \purple {\boxed {SA= \frac{2}{3} \pi rl+16 \pi r^2}} [/tex]
