# The generatrix of the cone, equal to 12 cm, is inclined to the base plane at an angle of 30 degrees. Find the volume of the cone.

January 26, 2021 | education

| Let’s draw the height of the cone. The height of the cone, the generatrix and the radius of the base form a right-angled triangle (the height is perpendicular to the base, and therefore perpendicular to the radius). In a right-angled triangle opposite an angle of 30 ° lies a leg, which is 2 times smaller than the hypotenuse. Therefore, the height of the cone is h = 6 cm.

Find the radius of the base by the Pythagorean theorem:

R = √ (12² – 6²) = √ (144 – 36) = √108.

The volume of the cone is calculated by the formula V = 1/3 * Sbn * h = 1/3 * пR² * h.

V = 1/3 * п * 108 * 6 = 216п.

Answer: the volume of the cone is 216п.

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