If we take the net of the cone, we have an sector with a radius equal to the cone's height, and a circle with a diameter equal to the cone's diameter.
In order to find the angle of the arc, we know that the circle's perimeter must equal the sector's arc.
\(P=\pi d\)\(l=\frac{\theta r}{2}\)
\(\frac{\theta r}{2}=\pi d\)
\(\frac{\theta 12}{2}=\pi 10\)
\(\theta=5.24rad\)
Area of circle base:
\(A=\pi r^2\)
\(A=\pi (\frac{10}{2})^2\)
\(A=78.54\)
Area of sector:
\(A=\frac{\theta r^2}{2}\)
\(A=\frac{5.24\times12^2}{2}\)
\(A=377\)
Total area is 456 units2
