Answer:
[tex]15\pi\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of the cone is equal to
[tex]LA=\pi rl[/tex]
where
r is the radius of the base
l is the slant height
we have
[tex]r=3\ cm[/tex]
Applying the Pythagoras Theorem find the slant height
[tex]l^{2}=3^{2} +4^{2}\\ \\l^{2}=25\\ \\l=5\ cm[/tex]
substitute in the formula
[tex]LA=\pi (3)(5)=15\pi\ cm^{2}[/tex]
