Answer:
[tex]x=5\ cm[/tex]
Step-by-step explanation:
we know that
The surface area of a cone is equal to
[tex]SA=\pi r^{2}+\pi rl[/tex]
where
r is the radius
l is the slant height
we have
[tex]SA=24\pi\ cm^2[/tex]
[tex]r=3\ cm\\l=x\ cm[/tex]
substitute the given values in the formula
[tex]24\pi=\pi (3)^{2}+\pi (3)x[/tex]
Simplify
[tex]24=9+3x[/tex]
solve for x
[tex]3x=24-9\\3x=15\\x=5\ cm[/tex]
