The axial section of the cone is a regular triangle with a side of 4 cm. Find the height of the cone.

Since the axial section of this cone is a regular triangle, this means that the diameter of the AC and the generators AB and BC are equal to each other.

Thus, the radius of the base is:

r = d / 2;

r = 4/2 = 2 cm.

The height of a regular triangle cuts it into two equal right-angled triangles. Consider one of them ∆ABO.

To calculate the height of the AO, we apply the Pythagorean theorem:

AB² = BO² + AO²;

BO² = AB² – AO²;

BO² = 4² – 2² = 16 – 4 = 12;

ВO = √12 = 3.5 cm.

Answer: The height of the cone is 3.5 cm.