In a truncated cone, the base radii are 8 and 34, and the axial section area is 168. Find the height and lateral surface area.

The axial section of a truncated cone is an isosceles trapezoid, which has the generatrix of the cone on its sides, and the diameters of the circles at the base at its bases.

Then Ssech = (AB + A1B1) * OO1 / 2.

OO1 = 2 * Ssech / (AB + A1B1) = 2 * 168/84 = 4 cm.

Let’s draw the height A1H of the axial section, the length of the segment AH = AO – HO = 34 – 8 = 26 cm.

In a right-angled triangle AA1H, AA12 = AH2 + HA12 = 676 + 16 = 692.

AA1 = √692 = 2 * √173 cm.

Let us determine the area of ​​the lateral surface of the cone.

Side = n * AA1 * (AO + A1O1) = n * 2 * √173 * (34 + 8) = n * 84 * √173 cm2.

Answer: The height of the cone is 4 cm, the lateral surface area is n * 84 * √173 cm2.