we have that
the formula to calculate the surface area of a cone is equal to
[tex]SA=\pi\cdot r\cdot l+\pi\cdot r^2[/tex]where
r is the radius of the circular base
l is the slant height
the formula to calculate the lateral area is equal to
[tex]LA=\pi\cdot r\cdot l[/tex]that means
[tex]SA=LA+\pi\cdot r^2[/tex]example
Find out the surface area and lateral area of a cone with
r=5 cm
h=10 cm
step 1
Find out the slant height (l)
Applying the Pythagorean Theorem
l^2=h^2+r^2
substitute given values
l^2=10^2+5^2
l^2=125
l=11.18 cm
step 2
Find out the lateral area
[tex]LA=\pi\cdot r\cdot l[/tex]substitute given values
[tex]\begin{gathered} LA=\pi\cdot5\cdot11.18 \\ LA=55.90\pi\text{ cm2} \end{gathered}[/tex]step 3
Find out the surface area
[tex]SA=LA+\pi\cdot r^2[/tex]substitute values
[tex]\begin{gathered} SA=55.90\pi+\pi\cdot5^2 \\ SA=55.90\pi+25\pi \\ SA=80.90\pi\text{ cm2} \end{gathered}[/tex]