The volume of the cone is 9√3pi cm3. Find the height of the cone if its axial section is an equilateral triangle.
| August 22, 2021 | education
The axial section of the cone is an equilateral triangle ABC, AB = BC = AC.
Let AB = BC = AC = X cm.
The height BО of an equilateral triangle is equal to: BО = АС * √3 / 2 = X * √3 / 2 cm.
The radius of the circle AO = AC / 2 = X / 2.
The volume of the cone is equal to:
V = 9 * π * √3 = π * AO ^ 2 * BO / 3 = π * (X ^ 2/4) * (X * √3 / 2) / 3.
9 = X ^ 3/24.
X ^ 3 = 216.
X = AB = BC = AC = 6 cm.
BО = 6 * √3 / 2 = 3 * √2 cm.
Answer: The height of the cone is 3 * √3 cm.
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