Question

find h. 9 ft h = √{?} ft 4 ft

Explanation:

Step1: Apply 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, $l = 9$ ft and $r = 4$ ft. We need to solve for $h$. Rearranging the formula gives $h=\sqrt{l^{2}-r^{2}}$.

Step2: Substitute values

Substitute $l = 9$ and $r = 4$ into the formula: $h=\sqrt{9^{2}-4^{2}}=\sqrt{81 - 16}$.

Step3: Calculate the result

$81-16 = 65$, so $h=\sqrt{65}$ ft.

Answer:

$\sqrt{65}$ ft