Find the volume of a regular triangular prism inscribed in a cylinder with a base radius of 2√3 and a height of 3√3.
| May 26, 2021 | education
Since the prism inscribed in the cylinder is regular, equilateral triangles lie at its base.
The radius of a circle circumscribed about an equilateral triangle is:
R = BC / √3.
BC = R * √3 = 2 * √3 * √3 = 6 cm.
The area of an equilateral triangle is:
Sас = ВС ^ 2 * √3 / 4 = 36 * √3 / 4 = 9 * √3 cm2.
Let us determine the volume of the inscribed prism.
Vpr = Sbn * АА1 = 9 * √3 * 3 * √3 = 81 cm3.
Answer: The volume of the inscribed prism is 81 cm3.
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