Question

find h. 12 cm h = √{?} cm 6 cm

Explanation:

Step1: Apply Pythagorean theorem

In a cone, if the slant - height is \(l\), the radius is \(r\), and the height is \(h\), then \(l^{2}=h^{2}+r^{2}\). Here, \(l = 12\) cm and \(r = 6\) cm. We need to solve for \(h\), so \(h=\sqrt{l^{2}-r^{2}}\).

Step2: Substitute values

Substitute \(l = 12\) and \(r = 6\) into the formula: \(h=\sqrt{12^{2}-6^{2}}=\sqrt{144 - 36}=\sqrt{108}\)

Answer:

\(\sqrt{108}\)