Question

find $ell$. $ell=sqrt{?}$ in.

Explanation:

Step1: Recall Pythagorean theorem

For a cone, the slant - height $\ell$, the radius $r$ and the height $h$ satisfy the Pythagorean theorem $\ell=\sqrt{h^{2}+r^{2}}$. Here, the radius $r = 6$ in and assume the height is not given but we can consider the right - triangle formed by the radius and the slant - height. If we assume the vertical height of the cone is $h$ and the slant - height is $\ell$, and the radius of the base is $r$. In this case, using the Pythagorean theorem with $r = 6$ in and if we assume the vertical height $h$ is related to the given non - radius length (assuming it is the vertical height) $h = 10$ in.

Step2: Calculate $\ell^{2}$

$\ell^{2}=10^{2}+6^{2}=100 + 36=136$.

Answer:

$\sqrt{136}$ in