The angle at the base of the axial section of the cone = b (beta) and the distance from the center of the base
| June 25, 2021 | education
The angle at the base of the axial section of the cone = b (beta) and the distance from the center of the base to the middle of the generatrix = a (alpha) find the volume of the cone
The axial section of the cone is an equilateral triangle ABC. Point O is the middle of AC, point M is the middle of AB, then OM is the middle line of triangle ABC, then BC = 2 * OM = 2 * α cm.
BCA angle = BAC = β.
The BOC triangle is rectangular, then OC = R = BC * Cosβ = 2 * α * Cosβ, OB = BC * Sinβ = 2 * α * Sinβ.
Determine the volume of the cone.
V = π * R2 * OB / 3 = π * 4 * α ^ 2 * Cos2β * 2 * α * Sinβ / 3 = 8 * π * α ^ 3 * Cos2β * Sinβ / 3 cm3.
Answer: The volume of the cone is 8 * π * α ^ 3 * Cos2β * Sinβ / 3 cm3.
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