The volume of the cone is 32. A plane parallel to the base is drawn through the middle
| September 25, 2021 | education
The volume of the cone is 32. A plane parallel to the base is drawn through the middle of the height of the cone. Find the volume cut off from the given cone by the plane.
Let the radius ОА = R1, А1О1 = R2, and the height ОВ = Н1. O1B = H2.
Triangles AOB and A1O1B are rectangular and similar in common angle B.
The coefficient of similarity of triangles is: K = ОВ / О1В = 2.
Then Н1 = 2 * Н2, R1 = 2 * R1.
The volume of the larger cone is: V1 = π * R1 ^ 2 * Н1 / 3 = π * 2 * R2 ^ 2 * 2 * Н2 / 3 = 32 cm3.
π * R2 ^ 2 * H2 / 3 = 32/4 = 8 cm3.
The volume of the cut-off cylinder is: V2 = π * R2 ^ 2 * H2 / 3 = 8 cm3.
Volume: The volume of the cut-off cylinder is 8 cm3.
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