Question

find h. 9 cm h = √? cm 8 cm

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, $l = 9$ cm and $r=\frac{8}{2}=4$ cm.

Step2: Rearrange the formula to solve for $h$

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

Step3: Calculate the value inside the square - root

$81-16 = 65$. So $h=\sqrt{65}$ cm.

Answer:

$\sqrt{65}$