Answer:
[tex]SA=76.8\ yd^2[/tex]
Step-by-step explanation:
step 1
Find the radius of the base of the cone
we know that
The lateral surface area of a cone is given by the formula
[tex]LA=\pi rl[/tex]
where
r is the radius of the base
l is the slant height
we have
[tex]l=2\ yd\\LA=62.8\ yd^2[/tex]
substitute
[tex]62.8=\pi r(2)[/tex]
assume
[tex]\pi=3.14[/tex]
[tex]62.8=(3.14)r(2)[/tex]
[tex]r=10\ yd[/tex]
step 2
Find the total surface area
we know that
The total surface area is given by
[tex]SA=\pi r^{2} +LA[/tex]
substitute the given values
[tex]SA=(3.14)(10^{2}) +62.8=376.8\ yd^2[/tex]
