To determine the slant height of the cone, we will apply the Pythagorean theorem to the right triangle ABC.
From the Pythagorean theorem we get that:
[tex]AC^2=AB^2+BC^2.[/tex]
We are given that:
[tex]\begin{gathered} BC=6in, \\ AB=\frac{4in}{2}=2in. \end{gathered}[/tex]
Therefore:
[tex]AC^2=(6in)^2+(2in)^2=36in^2+4in^2.[/tex]
Finally, solving for AC, we get:
[tex]AC=\sqrt{40in^2}=2\sqrt{10}\text{ in.}[/tex]
Answer:
[tex]\begin{equation*} 2\sqrt{10}\text{ in.} \end{equation*}[/tex]
