Answer:
The surface area of the cone is [tex]16\pi\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the radius
we know that
The lateral area of the cone is equal to
[tex]LA=\pi rl[/tex]
Let
x---------> the radius of the base of the cone
we have
[tex]LA=12\pi\ cm^{2}[/tex]
[tex]r=x\ cm[/tex]
[tex]l=3x\ cm[/tex]
substitute the values
[tex]12\pi=\pi (x)(3x)[/tex]
Simplify
[tex]3x^{2}=12\\x^{2}=4\\ x=2\ cm[/tex]
step 2
Find the surface area of the cone
The surface area of the cone is equal to
[tex]SA=LA+\pi r^{2}[/tex]
substitute the values
[tex]SA=12\pi+\pi (2)^{2}=16\pi\ cm^{2}[/tex]
