Answer:
[tex]7,561.12\ mm^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of a 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=80/2=40\ mm[/tex] ----> the radius is half the diameter
[tex]h=45\ mm[/tex]
To find the slant height apply the Pythagoras theorem
[tex]l^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]l^{2}=40^{2}+45^{2}[/tex]
[tex]l^{2}=3,625[/tex]
[tex]l=60.2\ mm[/tex]
Find the lateral area
assume [tex]\pi=3.14[/tex]
[tex]LA=(3.14)(40)(60.2)=7,561.12\ mm^{2}[/tex]
