The radii of the bases of the truncated cone are 5 dm and 10 dm, and the generatrix is 13 dm

The radii of the bases of the truncated cone are 5 dm and 10 dm, and the generatrix is 13 dm, find the height and area of its axial section.

The axial section of the truncated cone is an isosceles trapezoid. Let’s designate it ABCD. Its KM axis divides it into two, equal to each other, rectangular trapezoids.

To calculate the height of the ВН, consider the trapezoid ABKM. Angles ∠К and ∠М are straight.

The НM segment is equal to the length of the smaller radius:

НM = ВK = 5 dm.

Thus, the segment AH is equal to:

AН = AM – НM;

AH = 10 – 5 = 5 dm.

Using the Pythagorean theorem, we can find the length of the ВН height:

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

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 132 – 52 = 169 – 25 = 144;

BH = √144 = 12 cm.

Since the axial section is a trapezoid, its area is equal to:

S = (BC + AD) / 2 h;

S = (ВK + AM) h;

S = (5 + 10) 12 = 15 12 = 180 cm2.

Answer: the height of the cone is 12 cm, the area of ​​the axial section is 180 cm2.