Question

find h. 12 cm h = √{?} cm 6 cm

Explanation:

Step1: Apply Pythagorean theorem

For a cone, if the slant - height is $l = 12$ cm and the radius is $r = 6$ cm, and the height is $h$. According to the Pythagorean theorem $l^{2}=h^{2}+r^{2}$, so $h^{2}=l^{2}-r^{2}$.

Step2: Substitute values

Substitute $l = 12$ and $r = 6$ into the formula $h^{2}=l^{2}-r^{2}$. We get $h^{2}=12^{2}-6^{2}=144 - 36$.

Step3: Calculate the value of $h^{2}$

$144-36 = 108$.

Answer:

$h=\sqrt{108}$ cm