Question

use the image to answer the question.
find the length of the height of the cone.

Explanation:

Step1: Find the radius of the cone

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

Step2: Apply the Pythagorean theorem

For a right - triangle formed by the radius \(r\), height \(h\), and slant height \(l\) of the cone (\(l = 13\) cm), the Pythagorean theorem is \(h=\sqrt{l^{2}-r^{2}}\).
Substitute \(l = 13\) and \(r = 5\) into the formula: \(h=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}\).

Step3: Calculate the value of \(h\)

Since \(\sqrt{144}=12\).

Answer:

12 cm