The radii of the bases of the truncated cone are 11 cm and 6 cm, the generatrix is 13 cm. Find the volume of the cone.

univerkov | August 14, 2021 | education

Let’s draw the height BH of the cone.

Quadrangle BO1OH is a rectangle, then BO1 = OH = 6 cm.

AH = AO – OH = 11 – 6 = 5 cm.

In a right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the leg BH.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

BH = 12 cm.

Determine the volume of the truncated cone.

V = n * BH * (BO1 ^ 2 + BO1 * AO + AO ^ 2) / 3 = n * 12 * (36 + 66 + 121) / 3 = 12 * 223/3 = 892 cm3.

Answer: The volume of the truncated cone is 892 cm3.

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