For this problem, we need to calculate the surface area of a cone.
The surface area of a cone can be found with the following formula:
[tex]A=\pi r(r+\sqrt{h^2+r^2})[/tex]
We need to determine the height of the cone, we can use Pythagora's theorem to determine the height:
[tex]\begin{gathered} 13^2=h^2+5^2\\ \\ h^2=169-25\\ \\ h=\sqrt{144}=12 \end{gathered}[/tex]
Now we can determine the surface area:
[tex]\begin{gathered} A=\pi\cdot5\cdot(5+\sqrt{12^2+5^2})\\ \\ A=\pi\cdot5\cdot(5+\sqrt{144+25})\\ \\ A=\pi\cdot5\cdot(5+\sqrt{169})\\ \\ A=\pi\cdot5\cdot(5+13)\\ \\ A=\pi\cdot5\cdot18\\ \\ A=90\pi \end{gathered}[/tex]
The correct answer is B, 90pi.
