The radius of the base of the truncated cone is 3m and 6m, the height is 4m. Find the generatrix

The radius of the base of the truncated cone is 3m and 6m, the height is 4m. Find the generatrix length of the truncated cone

The axial section of the truncated cone has the shape of an isosceles trapezoid. For convenience, we will designate it ABCD.

The axis of this cone splits this trapezoid into two equal rectangular ones. Consider a trapezoid ABKM. Angles ∠К and ∠М are straight.

In this section, we will draw the height of the HВ. Thus, we get a right-angled triangle ΔАВН.

Since the НM segment is equal to the smaller base of the trapezoid, and is 3 cm, then:

AН = AM – НM;

AH = 6 – 3 = 3 cm.

To calculate AB, we apply the Pythagorean theorem:

AB ^ 2 = BH ^ 2 + AH ^ 2;

AB ^ 2 = 4 ^ 2 + 3 ^ 2 = 16 + 9 = 25;

AB = √25 = 5 cm.

Answer: the length of the generatrix of the truncated cone is 5 cm.