Question

find the height of this cone using the pythagorean theorem. h 8 cm h = √? cm 8 cm

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle in a cone, $l^{2}=h^{2}+r^{2}$, where $l$ is the slant height, $h$ is the height and $r$ is the radius. We need to solve for $h$, so $h=\sqrt{l^{2}-r^{2}}$.

Step2: Identify values of $l$ and $r$

The slant height $l = 8$ cm and the radius $r=\frac{8}{2}=4$ cm.

Step3: Calculate $h$

Substitute $l = 8$ and $r = 4$ into the formula $h=\sqrt{l^{2}-r^{2}}=\sqrt{8^{2}-4^{2}}=\sqrt{64 - 16}=\sqrt{48}$.

Answer:

$\sqrt{48}$