Surface area of the cone = 149.4π cm²
Step-by-step explanation:
Surface area of the cone is found using the radius and height as,
[tex]\mathrm{SA}=\pi r(r+\sqrt{\left(h^{2}+r^{2}\right)}[/tex]
From the given diameter, we can find the radius as,
radius = [tex]$\frac{12}{2}[/tex] = 6 cm
height = 18 cm
[tex]S A=\pi \times 6(6+\sqrt{\left(18^{2}+6^{2}\right)}[/tex]
[tex]\mathrm{SA}=6 \pi(6+\sqrt{(324+36)})[/tex]
[tex]$\mathrm{SA}=6 \pi(6+\sqrt{(360)})[/tex]
[tex]\mathrm{SA}=6 \pi(6+18.9)[/tex]
[tex]\mathrm{SA}=6 \pi(24.9)[/tex]
[tex]S A=149.4 \pi \mathrm{cm}^{2}[/tex]
