Question

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

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle related to a cone, if the slant height is $l$, the radius is $r$ and the height is $h$, then $l^{2}=h^{2}+r^{2}$, and $h = \sqrt{l^{2}-r^{2}}$.

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

Given that the slant height $l = 8$ cm and the diameter is 8 cm, so the radius $r=\frac{8}{2}=4$ cm.

Step3: Calculate height

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

Answer:

$\sqrt{48}$