Question

find h. h = \sqrt{?} in. 13 in 8 in

Explanation:

Step1: Recall Pythagorean theorem

For a cone, if the slant - height is $l$, the radius is $r$, and the height is $h$, then $l^{2}=h^{2}+r^{2}$. Here, $l = 13$ in and $r=\frac{8}{2}=4$ in.

Step2: Rearrange the formula for $h$

We can rewrite the Pythagorean formula as $h=\sqrt{l^{2}-r^{2}}$. Substitute $l = 13$ and $r = 4$ into the formula: $h=\sqrt{13^{2}-4^{2}}=\sqrt{169 - 16}$.

Step3: Calculate the value inside the square - root

$169-16 = 153$.

Answer:

$\sqrt{153}$