Question

find h. 13 in h = √{?} in. 12 in

Explanation:

Step1: Identify the right - triangle

The slant height of the cone ($l = 13$ in), the radius of the base ($r=6$ in as the diameter is 12 in so $r=\frac{12}{2}$), and the height of the cone ($h$) form a right - triangle. We use the Pythagorean theorem $l^{2}=h^{2}+r^{2}$.

Step2: Rearrange the Pythagorean theorem to solve for $h$

We get $h^{2}=l^{2}-r^{2}$. Substitute $l = 13$ and $r = 6$ into the formula: $h^{2}=13^{2}-6^{2}=169 - 36=133$.

Answer:

$\sqrt{133}$