Answer:
The lateral area of the cylinder is [tex]24 \pi\ units^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of the cylinder is equal to
[tex]LA=2\pi rh[/tex]
step 1
Find the radius of the base of the cylinder
The area of the base is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=36 \pi\ units^{2}[/tex]
so
substitute and solve for r
[tex]36 \pi=\pi r^{2}[/tex]
Simplify
[tex]r=6\ units[/tex]
step 2
Find the lateral area
we have
[tex]r=6\ units[/tex]
[tex]h=2\ units[/tex]
substitute the values
[tex]LA=2\pi (6)(2)=24 \pi\ units^{2}[/tex]
