In a truncated cone, the radius of the large base is 21cm, forming 39cm, the diagonal of the axial

In a truncated cone, the radius of the large base is 21cm, forming 39cm, the diagonal of the axial section is 45cm. Calculate the radius of the smaller base

The axial section of the prism is the isosceles trapezoid ABCD.

Let’s draw from the top B the height BH to the base AD.

Let us express, according to the Pythagorean theorem, the height of the ВН from two triangles, AВН and DBН.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 1521 – AH ^ 2.

BH ^ 2 = BD ^ 2 – DH ^ 2 = 2025 – (42 – AH) ^ 2.

Then 1521 – AH ^ 2 = 2025 – (1764 – 84 * AH + AH ^ 2).

1521 – AH ^ 2 = 2025 – 1764 + 84 * AH – AH ^ 2.

84 * AH = 1260.

AH = 1260/84 = 15 cm.

Then OH = AO – AN = 21 – 15 = 6 cm.

BO1 = OH = R = 6 cm.

Answer: The radius of the circle of the smaller base is 6 cm.