Question

find h. 10 cm h = √{?} cm 8 cm

Explanation:

Step1: Find the radius

The diameter is 8 cm, so the radius $r=\frac{8}{2}=4$ cm.

Step2: Apply Pythagorean theorem

In a cone, the slant - height $l = 10$ cm, radius $r = 4$ cm and height $h$ satisfy the Pythagorean theorem $l^{2}=h^{2}+r^{2}$. So $h^{2}=l^{2}-r^{2}$.
Substitute $l = 10$ and $r = 4$ into the formula: $h^{2}=10^{2}-4^{2}=100 - 16=84$.

Answer:

$\sqrt{84}$