Question

find the length of the height of the cone.
(1 point)
$square$ cm
the cone has a slant height of 13 cm, and the diameter of its base $d = 10$ cm.

Explanation:

Step1: Calculate base radius

The diameter $d=10$ cm, so radius $r=\frac{d}{2}=\frac{10}{2}=5$ cm.

Step2: Apply Pythagorean theorem

Let height = $h$, slant height $l=13$ cm. Use $h=\sqrt{l^2 - r^2}$.
$\displaystyle h=\sqrt{13^2 - 5^2}=\sqrt{169 - 25}=\sqrt{144}$

Step3: Simplify square root

$\sqrt{144}=12$

Answer:

12 cm