Answer:
Hence, the formula to find the modified surface area is:
\(9(\pi r^2+\pi rl)\)
i.e. it is 9 times the surface area of the original cone.
Step-by-step explanation:
We know that the surface area of a cone is given by the formula:
\(Surface\ Area(S)=\pi r^2+\pi rl\)
where r is the radius of the cone and l is the slant height of the cone.
Now we have that:
The slant height of the cone is tripled and the radius of a cone is also tripled.
i.e. r=3r
and l=3l
Hence, the modified surface area is given by:
\(Surface\ Area(S')=\pi (3r)^2+\pi (3r)\cdot (3l)\\\\\\S'=9\pi r^2+9\pi rl\\\\\\S'=9 (\pi r^2+\pi rl)\\\\\\S'=9 S\)
