We are going to calculate the area of paper neccesary to create the cone with 2 of radius, h=6 in
The area of the cone is:
[tex]A=\pi *r(r+a)[/tex]
We can find a using pitagoras:
[tex]\begin{gathered} a^2=h^2+r^2 \\ a=\sqrt[\placeholder{⬚}]{h^2+r^2}=\sqrt[\placeholder{⬚}]{6^2+2^2}=2\sqrt[\placeholder{⬚}]{10} \end{gathered}[/tex]
The area is:
[tex]\begin{gathered} A=\text{ }\pi *r*(r+a) \\ A=2\pi(2+2\sqrt[\placeholder{⬚}]{10}) \\ A=4\pi+4\pi\sqrt[\placeholder{⬚}]{10} \end{gathered}[/tex]
The answer is C.
