The radius of the base of the cone is 6 cm, and the axial section area is 42 cm. Find the height of the cone.

Since the cone is formed by rotating a right-angled triangle around one of the legs, its axial section will be an isosceles triangle.
For convenience, we will designate it as ABC. Since the area of a triangle is calculated as the product of the length of the base and the height lowered to it, we can find the height:

S = a * h;

h = S / a.

The base of our triangle is the same as the base diameter, which is twice the radius:

d = 2r;

d = a = 6 * 2 = 12 cm.

h = 42/12 = 3.5 cm.

Answer: The height of the cone is 3.5 centimeters.